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Visual Solutions

11 step-by-step animated solutions for Sequence & Series. Each solution breaks the problem into visual clips with key insights.

PYQ 2024 · Jan 29 Shift 1Easy5 steps
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to
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PYQ 2024 · Jan (1 Feb) Shift 1Standard4 steps
Let 3,a,b,c3, a, b, c be in A.P. and 3,a−1,b+1,c+93, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of aa, bb and cc is:
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PYQ 2024 · Jan (1 Feb) Shift 2Standard4 steps
Let SnS_n denote the sum of the first nn terms of an arithmetic progression. If S10=390S_{10} = 390 and the ratio of the tenth and the fifth terms is 15:715 : 7, then S15−S5S_{15} - S_5 is equal to:
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PYQ 2024 · Jan 27 Shift 2Standard4 steps
The 20th20^{\text{th}} term from the end of the progression 20,1914,1812,1734,…,−1291420, 19\frac{1}{4}, 18\frac{1}{2}, 17\frac{3}{4}, \ldots, -129\frac{1}{4} is:
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PYQ 2023 · Apr 6 Shift 1Standard4 steps
The sum of the first 20 terms of the series 5+11+19+29+41+…5 + 11 + 19 + 29 + 41 + \ldots is
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PYQ 2023 · Apr 10 Shift 1Standard4 steps
Let the first term aa and the common ratio rr of a geometric progression be positive integers. If the sum of squares of its first three terms is 3303333033, then the sum of these three terms is equal to
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PYQ 2023 · Apr 13 Shift 1Standard4 steps
Let s1,s2,…,s10s_1, s_2, \ldots, s_{10} respectively be the sum of 12 terms of 10 A.P.s whose first terms are 1,2,3,…,101, 2, 3, \ldots, 10 and the common differences are 1,3,5,…,191, 3, 5, \ldots, 19 respectively. Then ∑i=110si\sum_{i=1}^{10} s_i is equal to
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PYQ 2024 · Jan 31 Shift 1Tricky4 steps
The sum of the series 11−3⋅12+14+21−3⋅22+24+31−3⋅32+34+…\frac{1}{1-3 \cdot 1^2+1^4} + \frac{2}{1-3 \cdot 2^2+2^4} + \frac{3}{1-3 \cdot 3^2+3^4} + \ldots up to 10 terms is
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PYQ 2023 · Apr 13 Shift 2Tricky4 steps
Let a1,a2,a3,…a_1, a_2, a_3, \ldots be a G.P. of increasing positive numbers. Let the sum of its 6th6^{\text{th}} and 8th8^{\text{th}} terms be 2 and the product of its 3rd3^{\text{rd}} and 5th5^{\text{th}} terms be 19\frac{1}{9}. Then 6(a2+a4)(a4+a6)6(a_2 + a_4)(a_4 + a_6) is equal to
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PYQ 2024 · Apr 9 Shift 2Tricky4 steps
Let a,ar,ar2,…a, ar, ar^2, \ldots be an infinite G.P. If ∑n=0∞arn=57\sum_{n=0}^{\infty} ar^n = 57 and ∑n=0∞a3r3n=9747\sum_{n=0}^{\infty} a^3 r^{3n} = 9747, then a+18ra + 18r is equal to
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PYQ 2023 · Jan Shift 1Standard4 steps
The sum of the series 1+2⋅2+3⋅22+4⋅23+…+100⋅2991 + 2 \cdot 2 + 3 \cdot 2^2 + 4 \cdot 2^3 + \ldots + 100 \cdot 2^{99} is:
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