JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Numerical Value Type Questions - Sequences and Series Total Questions - 15

• question_answer1)
  Let \[{{a}_{1}},{{a}_{2}},.........,{{a}_{30}}\] be an A.P., \[S=\sum\limits_{i=1}^{30}{{{a}_{i}}}\] and  \[T=\sum\limits_{i=1}^{15}{{{a}_{(2i-1)}}.}\] If \[{{a}_{5}}=27\] and \[S-2T=75,\] then \[{{a}_{10}}\] is equal to
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• question_answer2)
  The sum of the following series \[1+6+\frac{9({{1}^{2}}+{{2}^{2}}+{{3}^{2}})}{7}+\frac{12({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}})}{9}\] \[+\frac{15({{1}^{2}}+{{2}^{2}}+....+{{5}^{2}})}{11}+....\] up to 15 terms, is:
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• question_answer3)
  Let \[{{S}_{n}}=1+q+{{q}^{2}}+......+{{q}^{n}}\] and \[{{T}_{n}}=1+\left( \frac{q+1}{2} \right)+{{\left( \frac{q+1}{2} \right)}^{2}}+.....+{{\left( \frac{q+1}{2} \right)}^{n}}\] where q is a real number and \[q\ne 1.\] If \[^{101}{{C}_{1}}{{+}^{101}}{{C}_{2}}.{{S}_{1}}+.....{{+}^{101}}{{C}_{101}}.{{S}_{100}}={{\alpha }^{100}}{{T}_{100}},\]then \[\alpha \] is equal to
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• question_answer4)
  Let \[{{a}_{1}},{{a}_{2}},{{a}_{3}}.......\] be terms on A.P. If \[\frac{{{a}_{1}}+{{a}_{2}}+.........{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+.........+{{a}_{q}}}=\frac{{{p}^{2}}}{{{q}^{2}}},\] \[p\ne q,\] if \[\frac{{{a}_{6}}}{{{a}_{21}}}\] equals \[\frac{11}{k}\] then k is
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• question_answer5)
  Fifth term of a GP is 2, then the product of its 9 terms is
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• question_answer6)
  The value of \[\sum\limits_{k=1}^{10}{\left( \sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11} \right)}\] is of the form \[{{i}^{k}},\] where k is smallest natural number, then k is
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• question_answer7)
  The value of \[{{2}^{1/4}}{{.4}^{1/8}}{{.8}^{1/16}}.....\infty \] is
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• question_answer8)
  The sum \[\sum\limits_{k=1}^{20}{k\frac{1}{{{2}^{k}}}}\] is equal to \[2-\frac{k}{{{2}^{19}}},\] then k is
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• question_answer9)
  If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then absolute value of its 11th term is 
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• question_answer10)
  If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},.......{{a}_{n}}\] are in A.P. and \[{{a}_{1}}+{{a}_{4}}+{{a}_{7}}+.....+{{a}_{16}}=114,\] then \[{{a}_{1}}+{{a}_{6}}+{{a}_{11}}+{{a}_{16}}\] is equal to
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• question_answer11)
  In the four numbers first three are in G.P. and last three are in A.P. whose common difference is 6. If the first and last numbers are same, then first number will be
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• question_answer12)
  If arithmetic mean of a and b is \[\frac{({{a}^{n+1}}+{{b}^{n+1}})}{{{a}^{n}}+{{b}^{n}}},\]then the value of n is equal to
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• question_answer13)
  The number of common terms to the two sequences 17, 21, 25,...... 417 and 16, 21, 26,........ 466 is
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• question_answer14)
  If product of three terms of a GP is 216, and sum of their products taken in pairs is 156, then greatest term is
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• question_answer15)
  If \[y={{3}^{x-1}}+{{3}^{-x-1}}\] (x real), then the least value of y is
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