JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Mock Test - Sequences and Series Total Questions - 25

• question_answer1)
  If \[{{S}_{n}}\]denotes the sum of first n terms of an A.P. and \[\frac{{{S}_{3n}}-{{S}_{n-1}}}{{{S}_{2n}}-{{S}_{2n-1}}}=31\], then the value of n is
  A)
  21         done clear
  B)
  15 done clear
  C)
  16                    done clear
  D)
  19 done clear
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• question_answer2)
  If x, y, z are real and \[4{{x}^{2}}+9{{y}^{2}}+16{{z}^{2}}-6xy-12yz-8zx=0\], then x, y, z are in
  A)
  A.P                   done clear
  B)
  G.P. done clear
  C)
  H.P.                 done clear
  D)
  none of these done clear
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• question_answer3)
  Consider the ten numbers \[ar,a{{r}^{2}},a{{r}^{3}},...a{{r}^{10}}\].If their sum is 18 and the sum the reciprocals is 6, then the product of these ten numbers is
  A)
  81                     done clear
  B)
  243 done clear
  C)
  343                  done clear
  D)
  324 done clear
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• question_answer4)
  If the sum of n terms of an A.P. is cn (n - 1), where \[c\ne 0\]then the sum of the squares of these term is
  A)
   \[{{c}^{n}}n{{(n+1)}^{2}}\] done clear
  B)
   \[\frac{2}{3}{{c}^{2}}n(n-1)(2n-1)\] done clear
  C)
   \[\frac{2{{c}^{2}}}{3}n(n+1)(2n+1)\] done clear
  D)
   none of these done clear
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• question_answer5)
  The largest term common to the sequences 1, 11, 21, 31 ,..to 100 terms and 31, 36, 41, 46,..to 100 terms is
  A)
  381 done clear
  B)
  471 done clear
  C)
  281                  done clear
  D)
  none of these done clear
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• question_answer6)
  If x, 2y, 3z are in A.P. where the distinct numbers x, y, z are in G.P., then the common ratio of the G.P. is
  A)
  3                      done clear
  B)
  \[\frac{1}{3}\] done clear
  C)
  2                     done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer7)
  If \[{{S}_{n}}\]denotes the sum of first n terms of an A.P. whose first term is a and \[{{S}_{nx}}/{{S}_{x}}\]is independent of x, then \[{{S}_{p}}=\]
  A)
  \[{{p}^{3}}\]              done clear
  B)
  \[{{p}^{2}}a\] done clear
  C)
  \[p{{a}^{2}}\] done clear
  D)
  \[{{a}^{3}}\] done clear
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• question_answer8)
  If a, b, and c are in A.P., p, q, and r are in H.P., and ap, bq, and cr are in G.P., then \[\frac{p}{r}+\frac{r}{p}\]is equal to
  A)
  \[\frac{a}{c}-\frac{c}{a}\]        done clear
  B)
  \[\frac{a}{c}+\frac{c}{a}\] done clear
  C)
  \[\frac{b}{q}+\frac{q}{b}\]       done clear
  D)
  \[\frac{b}{q}-\frac{q}{b}\] done clear
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• question_answer9)
  If \[{{a}_{1}},{{a}_{2}},{{a}_{3}}....{{a}_{n}}\]are in H.P. and \[f(k)=\left( \sum\limits_{r=1}^{n}{{{a}_{r}}} \right)-{{a}_{k}}\]then \[\frac{{{a}_{1}}}{f(1)},\frac{{{a}_{2}}}{f(2)},\frac{{{a}_{3}}}{f(3)},...\frac{{{a}_{n}}}{f(n)}\]are in
  A)
  A.P                   done clear
  B)
  G.P done clear
  C)
  H.P                  done clear
  D)
  none of these done clear
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• question_answer10)
  a, b, c, d,\[\in {{R}^{+}}\] such that a, b, and c are in A.P. and b, c and , d are in H.P., then
  A)
  ab = cd done clear
  B)
  ac = bd done clear
  C)
  bc = ad           done clear
  D)
  None of these done clear
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• question_answer11)
  if a, b, c are in A.P., then\[\frac{a}{bc},\frac{1}{c},\frac{2}{b}\] will be in
  A)
  A.P.                  done clear
  B)
  G.P. done clear
  C)
  H.P.                 done clear
  D)
  none of these done clear
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• question_answer12)
  The 15th terms of the series \[2\frac{1}{2}+1\frac{7}{13}+1\frac{1}{9}+\frac{20}{23}+...\]is
  A)
  \[\frac{10}{39}\]                       done clear
  B)
  \[\frac{10}{21}\] done clear
  C)
  \[\frac{10}{23}\]                       done clear
  D)
  none of these done clear
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• question_answer13)
  If \[{{x}_{1}},{{x}_{2}},.....{{x}_{20}}\]are in H.P. and \[{{x}_{1}},2,{{x}_{20}}\]are in G.P., then \[\sum\limits_{r=1}^{19}{{{x}_{r}}{{x}_{r+1}}}\]=
  A)
  76                     done clear
  B)
  80 done clear
  C)
  84                    done clear
  D)
  none of these done clear
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• question_answer14)
  Sum of the series \[\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+...\]to n terms is
  A)
  \[n-\frac{1}{2}({{3}^{n}}-1)\] done clear
  B)
  \[n+\frac{1}{2}({{3}^{n}}-1)\] done clear
  C)
  \[n+\frac{1}{2}(1-{{3}^{-n}})\] done clear
  D)
  \[n+\frac{1}{2}({{3}^{-n}}-1)\] done clear
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• question_answer15)
  The sum of the series \[\frac{x}{1-{{x}^{2}}}+\frac{{{x}^{2}}}{1-{{x}^{4}}}+\frac{{{x}^{4}}}{1-{{x}^{8}}}+...\]to infinite terms, if \[\left| x \right|<1\], is
  A)
  \[\frac{x}{1-x}\] done clear
  B)
  \[\frac{1}{1-x}\] done clear
  C)
  \[\frac{1+x}{1-x}\]                   done clear
  D)
  1 done clear
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• question_answer16)
  Let \[S=\frac{4}{19}+\frac{44}{{{19}^{2}}}+\frac{444}{{{19}^{3}}}+...\]up to \[\infty \]. Then S is equal to
  A)
  40/9                  done clear
  B)
  38/81 done clear
  C)
  36/171 done clear
  D)
  none of these done clear
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• question_answer17)
  The sum of 20 terms of the series whose rth term is given by \[T(n)={{(-1)}^{n}}\frac{{{n}^{2}}+n+1}{n!}\]is
  A)
  \[\frac{20}{19!}-2\]       done clear
  B)
  \[\frac{21}{20!}-1\] done clear
  C)
  \[\frac{21}{20!}\]                      done clear
  D)
  none of these done clear
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• question_answer18)
  If a, b, c and d are in H.P. then
  A)
   \[{{a}^{2}}+{{c}^{2}}>{{b}^{2}}+{{d}^{2}}\] done clear
  B)
   \[{{a}^{2}}+{{d}^{2}}>{{b}^{2}}+{{c}^{2}}\] done clear
  C)
   \[ac+bd>{{b}^{2}}+{{c}^{2}}\] done clear
  D)
   \[ac+bd>{{b}^{2}}+{{d}^{2}}\] done clear
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• question_answer19)
  If \[{{a}_{1}},{{a}_{2}}....{{a}_{n}}\]are in H.P., then the expression \[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}\]+...+\[{{a}_{n}}{{-}_{1}}{{a}_{n}}\]is equal to
  A)
  \[n({{a}_{1}}-{{a}_{n}})\]       done clear
  B)
  \[(n-1)({{a}_{1}}-{{a}_{n}})\] done clear
  C)
  \[n{{a}_{1}}{{a}_{n}}\]          done clear
  D)
  \[(n-1){{a}_{1}}{{a}_{n}}\] done clear
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• question_answer20)
  The sum of the series \[1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+...\]is
  A)
  \[\frac{e-1}{\sqrt{e}}\]   done clear
  B)
  \[\frac{e+1}{\sqrt{e}}\] done clear
  C)
  \[\frac{e-1}{2\sqrt{e}}\] done clear
  D)
  \[\frac{e+1}{2\sqrt{e}}\] done clear
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• question_answer21)
  \[{{1}^{3}}-{{2}^{3}}+{{3}^{3}}-{{4}^{3}}+...+{{9}^{3}}=\] ________.
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• question_answer22)
  The value of \[{{2}^{1/4}}\times {{4}^{1/8}}\times {{8}^{1/6}}.....\infty \,\]is _______.
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• question_answer23)
  The sum to 50 terms of the series\[1+2\left( 1+\frac{1}{50} \right)+3{{\left( 1+\frac{1}{50} \right)}^{2}}+...\] is given by __________.
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• question_answer24)
  The sum of 0.2+0.004+0.00006+0.0000008+...to \[\infty \]
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• question_answer25)
  If A.M., G.M., and H.M., of the first and last terms of the series 100, 101, 102,...n-1, n are the terms of the series itself, then the value of n is (100<n\[\le \]500) ________.
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