MAHARASHTRA Class 10: Sum of First n Terms of an A.P. Videos | Sum of n Terms of an A.P.

Let there be n terms in the given arithmetic series, then 

a_n= 30

⇒ a + (n − 1)d = 30

⇒ 6 + (n − 1) × 3 = 30

⇒ 6+ 3n − 3 = 30

⇒ 3n − 3 = 30

⇒ 3n = 33

⇒ n = 11

Therefore, the required sum of the series =11/2 [2 × 6 + (11− 1) × 3]

= 4.5 [12 + 10 × 3]

= 4.5 [12 + 30]

= 4.5 × 32

= 144 

The sum of the first n terms of the arithmetic progression whose first term = a and common difference = d is given by

Let there be n terms in the given arithmetic series, then 

a_n= 255

⇒ a + (n − 1)d = 255

⇒ 7 + (n − 1) × 8 = 255

⇒ 7 + 8n − 8 = 255

⇒ 8n − 1 = 255

⇒ 8n = 256

⇒ n = 32

Therefore, the required sum of the series =32/2[2 × 7 + (32 − 1) × 8]

= 16 [14 + 31 × 8]

= 16 [14 + 248]

= 16 × 262

= 4192