Sequences and Series PYQs - Last 5 Years
JEE Main / Mathematics / Algebra / 170 recent questions
MathematicsAlgebra2022-2026
Practice 170 JEE Main Mathematics questions from Sequences and Series. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
170
PYQs on Page
Mathematics / Algebra
2022-2026
Year Range
Based on indexed question metadata
170
Last 5 Years
2022-2026
170
Last 10 Years
2017-2026
Recent Year Trend
2022
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2026Latest year
202239 max PYQs/year2026
Question Types
170PYQs
MCQ64.7%
INTEGER35.3%
Difficulty Mix
#1 Medium146
#2 Hard16
#3 Easy8
170 in last 5 years170 in last 10 years
Last 5 Years Sequences and Series Questions
Showing 20 of 170 filtered questions.
1Sequences And Series
\(x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } }\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc \(\ne\) 0, then :
MCQ+4 / -12022
2Sequences And Series
If a1, a2, a3 ...... and b1, b2, b3 ....... are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4 b4 is equal to -
MCQ+4 / -12022
3Sequences And Series
Let \(S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,.....\). Then 4S is equal to
MCQ+4 / -12022
4Sequences And Series
Suppose \(a_{1}, a_{2}, \ldots, a_{n}\), .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is \(5: 17\) and , \(110 < {a_{15}} < 120\), then the...
MCQ+4 / -12022
5Sequences And Series
\(\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\cdots+
\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}\) is equal to _____________.
INTEGER+4 / -12022
6Sequences And Series
Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be \(\frac{98}{25}\). Then the sum of the first 21 terms of an AP, whose first term is $$10\mathrm{a r}, \mathrm{n}...
MCQ+4 / -12022
7Sequences And Series
If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to ___________.
INTEGER+4 / -12022
8Sequences And Series
If \(A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}\) and \(B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}\), then \({A \over B}\) is equal to :
MCQ+4 / -12022
9Sequences And Series
The series of positive multiples of 3 is divided into sets : \(\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots\) Then the sum of the elements in the \(11^{\text {th }}\) set is equal to ____________.
INTEGER+4 / -12022
10Sequences And Series
Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is \({(2)^{{{225} \over 8}}}\), then \(\sum\limits_{k = 1}^n {k(n - k)}\) is equal to :
MCQ+4 / -12022
11Sequences And Series
Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ___________.
INTEGER+4 / -12022
12Sequences And Series
If \(\sum\limits_{k=1}^{10} \frac{k}{k^{4}+k^{2}+1}=\frac{m}{n}\), where m and n are co-prime, then \(m+n\) is equal to _____________.
INTEGER+4 / -12022
13Sequences And Series
The greatest integer less than or equal to the sum of first 100 terms of the sequence \({1 \over 3},{5 \over 9},{{19} \over {27}},{{65} \over {81}},\) ...... is equal to ___________.
INTEGER+4 / -12022
14Sequences And Series
For a natural number n, let \({\alpha _n} = {19^n} - {12^n}\). Then, the value of \({{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}\) is ___________.
INTEGER+4 / -12022
15Sequences And Series
The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :
MCQ+4 / -12022
16Sequences And Series
Let \(a_{1}=b_{1}=1, a_{n}=a_{n-1}+2\) and \(b_{n}=a_{n}+b_{n-1}\) for every natural number \(n \geqslant 2\). Then \(\sum\limits_{n = 1}^{15} {{a_n}.{b_n}}\) is equal to ___________.
INTEGER+4 / -12022
17Sequences And Series
Let \(a, b\) be two non-zero real numbers. If \(p\) and \(r\) are the roots of the equation \(x^{2}-8 \mathrm{a} x+2 \mathrm{a}=0\) and \(\mathrm{q}\) and s are the roots of the equation \(x^{2}+12 \mathrm{~b} x+6 \mathrm{~b}=0\), such that...
INTEGER+4 / -12022
18Sequences And Series
The sum \(\sum\limits_{n = 1}^{21} {{3 \over {(4n - 1)(4n + 3)}}}\) is equal to
MCQ+4 / -12022
19Sequences And Series
If \(\{ {a_i}\} _{i = 1}^n\), where n is an even integer, is an arithmetic progression with common difference 1, and \(\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120}\), then n is equal to :
MCQ+4 / -12022
20Sequences And Series
Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
MCQ+4 / -12022