Question

Find the sum of the following arithmetic series:

(–5) + (–8) + (–11) + ... + (–230)

Answer 1

The given arithmetic series is (–5) + (–8) + (–11) + ... + (–230)

Here, a = –5, d = –8 – (–5) = –8 + 5 = –3 and `l` = 230.

Let the given series contain n terms. Then,

a_n = –230 

 ⇒ –5 + (n – 1) × (–3) = –230   ...[a_n = a + (n – 1)d]

⇒ –3n – 2 = –230 

⇒ –3n = –230 + 2 = –228 

⇒ n = 76 

∴ Required sum = `76/2 xx [(-5) + (-230)]`   ...`[S_n = n/2 (a + l)]`

= `76/2 xx (-235)`

= –8930