Let Sn denote the sum of first n-terms of an arithmetic progression.

Question

Let Sn 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

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

$= 2060 - 198$

$= 1862$

Solutions · 1