Find the sum of the first

(i) 11 terms of the A.P :

(ii) 13 terms of the A.P :

(iii) 51 terms of the A.P. whose second term is 2 and fourth term is 8.

(i) 11 terms of the A.P :

a = 2, d = 6 – 2 = 4

S₁₁= [2(a) + 10d]

= [2(2) + 10(4)]

= 11 [2 + 20]

= 242

(ii) 13 terms of the A.P :

a = -6, d = 0 + 6 = 6

S₁₃= [2(a) + 12d]

= 13 [-6 + 6(6)]

= 13 [-6 + 36]

= 13 (30) = 390

(iii) 51 terms of the A.P. whose second term is 2 and fourth term is 8.

a₂= 2

a + d = 2 (i)

a₄ = 8

a + 3d = 8

2 – d + 3d = 8

2 + 2d = 8

d = 3

a = -1

S₅₁= [2(a) + 50d]

= 51 [-1 + 25(3)]

= 51 (74)

= 3774