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Sums of an A.P. from given conditions on other sums

This type of question, asked 9 times: 2021 Paper 10, 2021 Paper 13, 2021 Paper 14, 2021 Paper 23, 30 Jan 2024, 1 Feb 2024, 23 Jan 2025, 24 Jan 2025, 22 Jan 2026 S1. All 9 questions below, oldest first.

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  1. Question 1

    2021 Paper 10

    69
    Let S1S_{1} be the sum of first 2n2n terms of an arithmetic progression. Let S2S_{2} be the sum of first 4n4n terms of the same arithmetic progression. If (S2−S1)\left( S_{2}-S_{1} \right) is 1000, then the sum of the first 6n6n terms of the arithmetic progression is equal to:

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  2. Question 2

    2021 Paper 13

    45
    Let sns_{n} denote sum of first nn-terms of ap, s10=530s_{10}= 530, s5=140s_{5}= 140, then s20−s6s_{20}-s_{6} is equal to

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  3. Question 3

    2021 Paper 14

    51
    In An A.P., S3n=3S2nS_{3n}= 3S_{2n}. Find S4nS2n\frac{S_{4n}}{S_{2n}}.

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  4. Question 4

    2021 Paper 23

    75
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be an A.P. If a1+a2+…+a10a1+a2+…+ap=100p2,p≠10\frac{a_{1}+a_{2}+ \ldots +a_{10}}{a_{1}+a_{2}+ \ldots +a_{p}}=\frac{100}{p^{2}},p\neq 10, then a11a10\frac{a_{11}}{a_{10}} is equal to :

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  5. Question 5

    30 Jan 2024

    62
    Let SnS_{n} denote the sum of first nn terms of an arithmetic progression. If S20=790S_{20}= 790 and S10=145S_{10}= 145, then S15−S_{15}- S5S_{5} is:

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  6. Question 6

    1 Feb 2024

    160
    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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  7. Question 7

    23 Jan 2025

    58
    If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

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  8. Question 8

    24 Jan 2025

    134
    In an arithmetic progression, if S40=1030S_{40}= 1030 and S12=57S_{12}= 57, then S30−S10S_{30}-S_{10} is equal to:

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  9. Question 9

    22 Jan 2026 S1

    70
    If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4 , then the sum of its first twelve terms is

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