Question

Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n = 5 – 2n.

Find the sum of the first 20 terms of an A.P. whose n^th term is given by a_n = 5 – 2n.

Answer 1

We have, a_n = 5 – 2n

∴ a₁ = 5 – 2 = 3

and a₂ = 5 – 4 = 1

∴ d(common difference) = 1 – 3 = –2

Now, S₂₀ = `20/2[2 xx 3 + (20 - 1)(-2)]`  ......`[∵ S_n = n/2[2a + (n - 1)d]]`

= 10[6 – 19 × 2]

= 10[6 – 38]

= 10 × (–32)

= –320