Question

In an A.P, the sum of first ten terms is -80 and the sum of its next ten terms is -280.
Find the A.P

Answer 1

Sum of first ten terms is -80.

Sum of next ten terms is -280.

So sum of first twenty terms is -360.

Sum of first n terms of an AP

$S_n = \frac{n}{2}(2a + [n-1]d)$

where a is the first term and d is common difference.

$S_{10} = \frac{10}{2} [2a + (10-1)d] = -80$

$2a + 9d = -16.....(i)$

$S_{20} = \frac{20}{2}[2a + (20-1)d] = -360$

$2a + 19d = -36.....(ii)$

$\small\black\boxed{(ii)-(i)}$

$10d = -20$

$d = -2$

Substitute the value of d in equation (i)

$2a - 18 = -16$

$a = 1$

So the AP is

1 , -1 , -3 , -5 , -7.....

Answer 2

Answer:

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