JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Numerical Value Type Questions - Progressions Total Questions - 15

• question_answer1)
  If \[{{S}_{1}},\text{ }{{\text{S}}_{2}},\text{ }{{S}_{3}}\] are the sums of first n natural numbers, their squares, their cubes respectively, then find the value of \[\frac{{{S}_{3}}\left( 1+8{{S}_{1}} \right)}{{{S}_{2}}^{2}}\] .
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• question_answer2)
  Let \[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1+2}{{{1}^{3}}+{{2}^{3}}}+...+\frac{1+2+....+n}{{{1}^{3}}+{{2}^{3}}+....+{{n}^{3}}};n=1,2,3...\] Then find maximum value of\[{{S}_{n}}\].
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• question_answer3)
  A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way and this process continuous indefiniting. If a side of the first square is 4 cm and the sum of the area of all the squares is \[\alpha \] then find the value of \[\alpha /4\].
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• question_answer4)
  Let 'p' and 'q' be the roots of the equation \[{{x}^{2}}-2x+A=0\], and Let 'r' and 's' be the roots of the equation \[{{x}^{2}}-18x+B=0\]. If \[p<q<r<s\] are in A.P. then find value of \[\left( A+B \right)\].
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• question_answer5)
  Find the number of terms common to the two sequences 17, 21, 25, ...., 417 and 16, 21, 26, ...., 466.
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• question_answer6)
  The repeating decimal 0.429642964296.... represents the fraction\[\frac{m}{3333}\]then find value of m.
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• question_answer7)
  Between 1 and 31 are inserted m arithmetic means, so that the ratio of the 7th and\[(m-1)th\] means is 5 : 9. Then find the value of m.
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• question_answer8)
  If the ratio of sum of n terms of two different A.P's is \[\frac{3n+5}{4n+3}\] then find the ratio of their 7th terms.
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• question_answer9)
  Find the maximum value of the sum of the A.P. 30, 27, 24, 21, .....
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• question_answer10)
  If the sum of positive terms of the series \[10+9\frac{4}{7}+9\frac{1}{7}+.....is\,\frac{k}{7}\]then find value of k.
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• question_answer11)
  If \[{{a}_{1}},{{a}_{2}}...,{{a}_{15}}\] are in A.P. and \[{{a}_{1}}+{{a}_{8}}+{{a}_{15}}=15,\] then \[{{a}_{2}}+{{a}_{3}}+{{a}_{8}}+{{a}_{13}}+{{a}_{14}}=\]
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• question_answer12)
  Let \[{{a}_{n}}\] be the nth term of an A.P. If \[\sum\limits_{r=1}^{100}{{{a}_{2r}}}=\alpha \] and \[\sum\limits_{r=1}^{100}{{{a}_{2r-1}}}=\beta \], and the common difference of A.P. is \[\frac{\alpha -\beta }{\lambda }\] then find \[\lambda \].
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• question_answer13)
  Sum of first n positive terms of an A.P. is given by\[{{S}_{n}}=\left( 1+2{{T}_{n}} \right)\left( 1-{{T}_{n}} \right)\]. If the value of \[{{T}_{2}}^{2}\] is \[\frac{\sqrt{2}-1}{k\sqrt{2}}\] then find k.
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• question_answer14)
  If \[\frac{3+5+7+.........+\left( 2n-1 \right)}{5+8+11+..........10\,terms}=7\] then find value of n.
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• question_answer15)
  Find sum of the series \[S=1+\frac{1}{2}\left( 1+2 \right)+\frac{1}{3}\left( 1+2+3 \right)+\frac{1}{4}\left( 1+2+3+4 \right)+....\]Upto 20 terms.
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