Question

Find the sum of the following arithmetic series:

34 + 32 + 30 + ... + 10

Answer 1

The given arithmetic series is 34 + 32 + 30 + ... + 10.

Here, a = 34, d = 32 – 34 = –2 and `l` = 10.

Let the given series contain n terms. Then,

a_n = 10 

⇒ 34 + (n – 1) × (–2) = 10   ...[a_n = a + (n – 1)d]

⇒ –2n + 36 = 10 

⇒ –2n = 10 – 36 = –26

⇒ n = 13 

∴ Required sum = `13/2 xx (34 + 10)`   ...`[S_n = n/2 (a + l)]`

= `13/2 xx 44 `

= 286