Find the sum of each arithmetic series

(i) 38 + 35 + 32 + … + 2. (ii) terms.

(i) In the A.P.

First term = 38

Last term = 2

Common difference = 35–38 = –3

Nth term = a + (n–1) d

⇒ 2 = 38 + (n–1)(–3)

⇒ –36 = (n–1)(–3)

⇒ 12 = (n–1)

⇒ n = 13

Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms = 260

(ii) In the A.P.

First term = 6

No. of terms = 25

Common difference = 21/4 – 6 = –3/4

Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms = –75