10th Class Mathematics Arithmetic Progressions Question Bank

done Arithmetic Progressions Total Questions - 55

• question_answer1)
  Find the general term of the series 4,7, 10,13......
  A)
   3n - 7                                    done clear
  B)
   3n + 7 done clear
  C)
   3n +1     done clear
  D)
          3n ? 1 done clear
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• question_answer2)
  Which is the first negative term of the arithmetic progression 35, 30, 25,.....?
  A)
   7th term        done clear
  B)
          5th term done clear
  C)
   9th term        done clear
  D)
          11th term done clear
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• question_answer3)
  Find the next term of the arithmetic progression \[\sqrt{12},\sqrt{27},\sqrt{48}\]
  A)
   \[\sqrt{75}\]     done clear
  B)
                          \[\sqrt{60}\] done clear
  C)
   \[\sqrt{80}\]                      done clear
  D)
          \[\sqrt{90}\] done clear
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• question_answer4)
  What is the term of an arithmetic progression whose sum to 'n' terms is\[2{{n}^{2}}-3n\]?
  A)
   4n - 3                    done clear
  B)
          4n ? 5 done clear
  C)
   4n + 5                   done clear
  D)
          5 - 4n done clear
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• question_answer5)
  Which term of the arithmetic progression 30, 27, 24,.... is O?
  A)
   8th term        done clear
  B)
          10th term done clear
  C)
   13th term      done clear
  D)
          11th term done clear
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• question_answer6)
  The numbers 28, 22, 'x', 'y', 4 are in arithmetic progression. What are the respective values of 'x' and 'y'?
  A)
   10, 16                                   done clear
  B)
   20, 18 done clear
  C)
   18, 16                                   done clear
  D)
   16, 10 done clear
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• question_answer7)
  What is the sum to 'n' terms of the series\[\sqrt{5},\sqrt{20},\sqrt{45},\sqrt{80},.....?\]
  A)
   \[\frac{n(n+1)\sqrt{5}}{2}\]        done clear
  B)
          \[\frac{n(n+1)}{\sqrt{2}}\] done clear
  C)
   \[\frac{n}{2}\left( \frac{(n+1)}{\sqrt{5}} \right)\]              done clear
  D)
          \[n(n+1)\sqrt{5}\] done clear
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• question_answer8)
  What is the sum of the first 'n' even numbers?
  A)
   \[{{n}^{2}}+1\] done clear
  B)
          \[n(n-1)\] done clear
  C)
   \[{{n}^{2}}-n\]  done clear
  D)
          \[n(n+1)\] done clear
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• question_answer9)
  What is the sum of first 'n' odd numbers starting from 11?
  A)
   \[{{n}^{2}}+10n\]            done clear
  B)
          \[{{n}^{2}}-10n\] done clear
  C)
   \[10n-{{n}^{2}}\]             done clear
  D)
          \[{{n}^{2}}\] done clear
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• question_answer10)
  How many two digit numbers are divisible by 4?
  A)
   20            done clear
  B)
                          16 done clear
  C)
   25                          done clear
  D)
          22 done clear
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• question_answer11)
  How many terms of the arithmetic progression 1, 9, 17, .... must be taken to give a sum of 1540?
  A)
   10                          done clear
  B)
          40 done clear
  C)
   20                          done clear
  D)
          15 done clear
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• question_answer12)
  What is the sum of 36 terms of the series whose\[{{n}^{th}}\]term is 5n + 4?
  A)
   4347                      done clear
  B)
          3474 done clear
  C)
   4374                      done clear
  D)
          3447 done clear
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• question_answer13)
  Divide 21 into three parts that are in arithmetic progression and whose product is 168.
  A)
   3, 6, 9                   done clear
  B)
          14, 17, 11 done clear
  C)
   2, 6, 14                 done clear
  D)
          2, 7, 12 done clear
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• question_answer14)
  Which term of the arithmetic progression 3, 8, 13, ..... is 55 more than its 20th term?
  A)
   29th term       done clear
  B)
          31st term done clear
  C)
   25th term       done clear
  D)
          27th term done clear
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• question_answer15)
  Identify the formula for then\[{{n}^{th}}\]term of the arithmetic progression whose first term, [a] is 2 - x, and the common difference, [d] is 'x'.
  A)
   \[2+x-nx\]          done clear
  B)
          \[2+(n-2)x\] done clear
  C)
   \[2-x-nx\]           done clear
  D)
          \[2+(n-1)x\] done clear
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• question_answer16)
  Find the number of terms of the arithmetic progression\[\frac{1}{3},\frac{1}{2},\frac{2}{3},......\frac{11}{6}\]
  A)
   8                             done clear
  B)
          10 done clear
  C)
   12                          done clear
  D)
          13 done clear
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• question_answer17)
  The first, second and last terms of an arithmetic progression are 5, 9 and 101 respectively. Find the number of terms in the arithmetic progression.
  A)
   30                                          done clear
  B)
   50   done clear
  C)
   25                                          done clear
  D)
   75 done clear
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• question_answer18)
  Find the sum of the first 18 terms, of the arithmetic progression 12b, 8b, 4b,......
  A)
   126b                                     done clear
  B)
   -56b done clear
  C)
   256b                     done clear
  D)
          - 288b done clear
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• question_answer19)
  Find the sum of the arithmetic progression, \[x-2y,2x-y,3x......11x+8y\].
  A)
   \[33(2x+y)\]                      done clear
  B)
   \[22(2x+y)\] done clear
  C)
   \[28(x+y)\]        done clear
  D)
          \[33x+11y\] done clear
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• question_answer20)
  Find the sum from the sixth term to the twelfth term of the arithmetic progression 6, 10, 14, ....
  A)
   176                                        done clear
  B)
   232 done clear
  C)
   266                                        done clear
  D)
   184 done clear
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• question_answer21)
  The first term and the common difference of an arithmetic progression are 13 and 5 respectively. Find the sum from the 6th term to the 20th term.
  A)
   876                        done clear
  B)
          146 done clear
  C)
   1095                      done clear
  D)
          1080 done clear
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• question_answer22)
  Find the value of 'n' if the sum of the first 'n' terms of the A.P.I 5, 23, 31, ....... is 708.
  A)
   9                             done clear
  B)
          8 done clear
  C)
   12                          done clear
  D)
          10 done clear
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• question_answer23)
  A piece of wire is used to make circles of the following pattern. The radius of the first circle is 'r' cm and it is increased by 1 cm successively. Find the length of the wire that is required to make 5 such circles.
  A)
   \[(10\pi +r)cm\]               done clear
  B)
   \[2\pi \,cm\] done clear
  C)
   \[10\pi (r+2)\,cm\]         done clear
  D)
   \[2\pi (r+2)\,cm\] done clear
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• question_answer24)
  An arithmetic progression has a 3rd term of 13 and a last term of 148. If the common difference is 5, find the number of terms of the progression.
  A)
   30                          done clear
  B)
          40   done clear
  C)
   50                          done clear
  D)
          75 done clear
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• question_answer25)
  Given that the sum of the first 'n' terms of an arithmetic progression is 2n2 + 3n, find the twelfth term.
  A)
   \[{{7}^{2}}\]                      done clear
  B)
          \[36\] done clear
  C)
   \[\sqrt{625}\]                   done clear
  D)
          56 done clear
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• question_answer26)
  The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added to get - 30?
  A)
   15                          done clear
  B)
          20   done clear
  C)
   25                          done clear
  D)
          18 done clear
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• question_answer27)
  A secondary school had an enrolment of 1620 students in the year 2009 which increases by 150 students per year. What was the enrolment in the year 2013?
  A)
   2170                      done clear
  B)
          2070 done clear
  C)
   2220                      done clear
  D)
          2150 done clear
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• question_answer28)
  A piece of wire is used to make rectangles with the same height of 'h' cm. The lengths of the rectangles are increased by 1 cm successively. Find the total length of wire required to make 7 rectangles in this pattern.
  A)
   \[\text{2 }\!\![\!\!\text{ h }+\text{ b }+\text{ 7 }\!\!]\!\!\text{ }\]    done clear
  B)
          2b + h + 7 done clear
  C)
   2n + h + 6            done clear
  D)
          \[\text{2 }\!\![\!\!\text{ b }+\text{ h }+\text{ 6 }\!\!]\!\!\text{ }\] done clear
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• question_answer29)
  The postal rates in India from town M to town N are tabulated as shown.

  Weight (g)	1-60	61-80	81-100	101-120	121-140
  Postal Rate(Rs.)	3.00	3.50	4.00	4.50	5.00

  Amir posts a 230 g parcel from town M to town N, what is the postal charge?
  A)
   Rs. 8.00                done clear
  B)
          Rs. 7.50 done clear
  C)
   Rs. 7.00                done clear
  D)
          Rs. 6.00 done clear
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• question_answer30)
  A cineplex has 13 rows of seats with 10 seats in the first row, 12 in the second, 14 in the third and so on. What is the total number of seats in the cineplex?
  A)
   252                        done clear
  B)
          256 done clear
  C)
   258                        done clear
  D)
          286 done clear
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• question_answer31)
  Sulekha intends to read a 200 page book within a specific period-She starts by reading 11 pages on the first day and increases her rate of reading by reading an extra 2 pages for each subsequent day How long will she take to finish reading the book?
  A)
   20                          done clear
  B)
          10 done clear
  C)
   15                                          done clear
  D)
   25 done clear
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• question_answer32)
  The 6th term of an arithmetic progression is 30 and the sum of the first six terms is 210. Find the sum of the next 6 consecutive terms.
  A)
   100                        done clear
  B)
          50 done clear
  C)
   138                        done clear
  D)
          204 done clear
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• question_answer33)
  The given figure shows a pattern of several squares drawn consecutively. The perimeters of the squares in figure form an arithmetic progression. The length of the first square is x cm and the length of the other consecutive squares differ from each other by 1 cm. Given the sum of the perimeters of the first five squares is 160 cm, find the sum of the perimeters of the first 10 squares.
  A)
   280 cm                                 done clear
  B)
   240 cm done clear
  C)
   420 cm                 done clear
  D)
          360 cm done clear
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• question_answer34)
  In an arithmetic progression, the fourth term is 8 and the sum of 12 terms is 156. Find the value of 'p' if the \[{{p}^{th}}\]term is 1000.
  A)
   200                        done clear
  B)
          500 done clear
  C)
   300                        done clear
  D)
          100 done clear
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• question_answer35)
  A roll of thread 907i cm long is cut into 5 parts to make up 5 circles as shown in the figure. The radii of the circles increase by 1 cm consecutively. Find the radius of the smallest circle.
  A)
   7 cm                                      done clear
  B)
   5 cm done clear
  C)
   6 cm                      done clear
  D)
          9 cm done clear
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• question_answer36)
  A circle is divided into 18 sectors such that the angles subtended at the centre form an arithmetic progression. Given that the angle of the smallest sector is\[\text{11}.\text{5}{}^\circ \], find the angle of the biggest sector.
  A)
   \[\text{3}0{}^\circ \]                                      done clear
  B)
   \[\text{15}.\text{5}{}^\circ \] done clear
  C)
   \[\text{45}{}^\circ \]                      done clear
  D)
          \[\text{28}.\text{5}{}^\circ \] done clear
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• question_answer37)
  An arithmetic progression has 10 terms. The sum of the odd terms is 245 whereas the sum of the even terms is 305. Find the common difference.
  A)
   2                                             done clear
  B)
   7 done clear
  C)
   3                                             done clear
  D)
   1 done clear
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• question_answer38)
  Given an arithmetic progression -10,-5,0,..... Identify three consecutive terms of the progression whose sum is 90.
  A)
   26, 31, 36            done clear
  B)
   25, 30, 35 done clear
  C)
   20, 30, 40      done clear
  D)
          18, 23, 28 done clear
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• question_answer39)
  The first three terms of a sequence are 8, 'y' and 18. Find the positive value of 'y' so that the sequence is an arithmetic progression.
  A)
   26                                          done clear
  B)
   18 done clear
  C)
   12                          done clear
  D)
          13 done clear
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• question_answer40)
  The sum of the first 10 terms of an arithmetic progression is four times the sum of its first five terms. Find the ratio of the first term to the common difference.
  A)
   1:4                                         done clear
  B)
   4:1 done clear
  C)
   2:1                         done clear
  D)
          1:2 done clear
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• question_answer41)
  How many numbers between 100 and 1000 are divisible by 7?
  A)
   7                                             done clear
  B)
   128 done clear
  C)
   132                                        done clear
  D)
   127 done clear
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• question_answer42)
  Find the sum of 14 AM's between 5 and 8.
  A)
   91                          done clear
  B)
          89 done clear
  C)
   90                          done clear
  D)
          85 done clear
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• question_answer43)
  If\[{{\text{1}}^{\text{3}}}+{{\text{2}}^{\text{3}}}+.....+{{\text{m}}^{\text{3}}}=\text{3}0\text{25}\], find m.
  A)
   12                          done clear
  B)
          10   done clear
  C)
   17                          done clear
  D)
          12 done clear
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• question_answer44)
  If\[{{m}^{th}}\]term of an arithmetic progression is 'n' and\[{{n}^{th}}\]term is 'm', find its\[{{(m+n)}^{th}}\]term.
  A)
   0                             done clear
  B)
          \[\text{m}+\text{n}-\text{p}\] done clear
  C)
   \[\text{m}+\text{n}\]                   done clear
  D)
          \[\frac{mn}{m+n}\] done clear
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• question_answer45)
  The sum to 'n' natural numbers is \[{{S}_{1}}\] sum of the squares of 'n' natural numbers is \[{{S}_{2}}\] and sum of the cubes of 'n' natural numbers is \[{{S}_{3}}\] Which of the following is equal to \[9S_{2}^{2}\]?
  A)
   \[(1-8{{S}_{1}}){{S}_{2}}\]           done clear
  B)
          \[{{S}_{3}}(1+8{{S}_{1}})\] done clear
  C)
   \[{{S}_{1}}(1+8{{S}_{2}})\]                          done clear
  D)
   \[{{S}_{1}}(1-8{{S}_{3}})\] done clear
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• question_answer46)
  In an arithmetic progression if 7 times the 7th term is equal to 11 times the 11th term, find its 18th term.
  A)
   1                             done clear
  B)
          0 done clear
  C)
   -1                           done clear
  D)
          2 done clear
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• question_answer47)
  Find the sum of the numbers in between 1 and 1000 which are divisible by 9.
  A)
   55944                                   done clear
  B)
   54954 done clear
  C)
   99994                   done clear
  D)
          99894 done clear
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• question_answer48)
  There are 'n' arithmetic means in between 'a' and 'b'. Find the common difference.
  A)
   \[\frac{b-a}{n+1}\]                         done clear
  B)
   \[\frac{b+a}{n-1}\] done clear
  C)
   \[\frac{b-a}{n-1}\]          done clear
  D)
          \[\frac{b+a}{n+1}\] done clear
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• question_answer49)
  What is the sum of 'n' arithmetic means between 'a' and 'b'?
  A)
   \[\frac{3}{2}(a+2b)\]     done clear
  B)
          \[\frac{n}{2}[a+b]\] done clear
  C)
   \[\frac{n}{2}[a-b]\]        done clear
  D)
          \[\frac{n}{4}[a+b]\] done clear
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• question_answer50)
  Find the sum of\[\left( 1-\frac{1}{n} \right)+\left( 1-\frac{2}{n} \right)+\left( 1-\frac{3}{n} \right)....\]terms.
  A)
   \[\frac{n}{2}\]                         done clear
  B)
         \[\frac{n-1}{2}\] done clear
  C)
   \[\frac{n+1}{2}\]             done clear
  D)
          \[\frac{n(n+1)}{{{n}^{2}}}\] done clear
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• question_answer51)
  In an arithmetic progression, if\[{{\text{t}}_{\text{p}}}\text{=q},{{\text{t}}_{\text{q}}}=\text{p},\]find \[{{\text{t}}_{\text{pq}}}\].
  A)
   \[\text{p}+\text{q}-\text{pq}\]                done clear
  B)
          \[\text{p}+\text{q}\] done clear
  C)
   \[~\text{p}-\text{q}+\text{pq}\]             done clear
  D)
          \[\text{pq}-\text{p}-\text{q}\] done clear
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• question_answer52)
  Find three numbers in arithmetic progression whose sum is 3 and product is-35.
  A)
   \[\text{1},\text{5},\text{7}\]                     done clear
  B)
          \[-\text{5},\text{7},-\text{1}\] done clear
  C)
   \[-\text{5},\text{1},\text{7}\]                   done clear
  D)
          \[-\text{7},\text{5},-\text{1}\] done clear
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• question_answer53)
  Which of the following is incorrect?
  A)
   \[{{S}_{n}}\]of the arithmetic progression 3, \[13,23,....\]is\[5{{n}^{2}}-8n\]. done clear
  B)
   \[{{S}_{n}}=3{{n}^{2}}-8n\]is the sum of an arithmetic progression whose common difference is 6. done clear
  C)
   \[{{n}^{th}}\]term, \[{{t}_{n}}={{s}_{n}}-{{s}_{n-1}}\] done clear
  D)
   The\[{{n}^{th}}\]term of an arithmetic progression is \[{{t}_{n}}=a+(n-1)d\]. done clear
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• question_answer54)
  Given P=3+5+7+ .... (n terms) and Q = 5 + 8 +11 +..... (10 terms).What is the value of 'n' if\[\frac{P}{Q}=7\]?
  A)
   25                          done clear
  B)
          35   done clear
  C)
   30                          done clear
  D)
          20 done clear
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• question_answer55)
  What is the value of 'x' if\[2x,x+10\]and\[3x+2\]are in arithmetic progression?
  A)
   5                             done clear
  B)
          6    done clear
  C)
   4                             done clear
  D)
          -6 done clear
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