QJEEM21Ma8575: JEE Main 2021 Mathematics - Class 11 JEEM21Ma8575 Solution: Let S n denote the sum of first n-terms of an arithmetic…

Question

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Let S_n denote the sum of first n-terms of an arithmetic progression. If S₁₀ = 530, S₅ = 140, then S₂₀

-

S₆ is equal to:

Accepted Answer

Let first term of A.P. be a and common difference is d.

\therefore

{S_{10}} = {{10} \over 2}\{ 2a + 9d\} = 530

\therefore

2a + 9d = 106

..... (i)

{S_5} = {5 \over 2}\{ 2a + 4d\} = 140

a + 2d = 28

...... (ii)

From equation (i) and (ii), a = 8, d = 10

\therefore

{S_{20}} - {S_6} = {{20} \over 2}\{ 2 \times 8 + 19 \times 10\} - {6 \over 2}\{ 2 \times 8 + 5 \times 10\}

= 2060 - 198

= 1862

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