Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.

First term = a

Common difference = d

3^rd term = a + (3–1)d = a + 2d

7^th term = a + (7–1)d = a + 6d

Now, 3^rd term = 7

⇒ a + 2d = 7 ………………………(1)

And, 7^th term = 3 × (3^rd term) + 2

⇒ a + 6d = 3(a + 2d) + 2

⇒ a + 6d = 3a + 6d + 2

⇒ 2a = –2

⇒ a = –1

Putting value of a in (1)

(⇒ –1) + 2d = 7

⇒ 2d = 8

⇒ d = 4

Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms = 740