Find the sum of the first (i) 11 terms of the A.P : 2,6,10,14, ....(i

1.	Find the sum of the first (i) 11 terms of the A.P : 2,6,10,14, ....(ii) 13 terms of the A.P : -6,0,6,12,....(iii) 51 terms of the A.P. whose second term is 2 and fourth term is 8.
Answer» (i) a = 2, d = 6 – 2 = 4 S₁₁=\(\frac{11}{2}\) [2(a) + 10d] = \(\frac{11}{2}\)[2(2) + 10(4)] = 11 [2 + 20] = 242 (ii) a = -6, d = 0 + 6 = 6 S₁₃= \(\frac{13}{2}\)[2(a) + 12d] = 13 [-6 + 6(6)] = 13 [-6 + 36] = 13 (30) = 390 (iii) a₂= 2 a + d = 2 (i) a₄= 8 a + 3d = 8 2 – d + 3d = 8 2 + 2d = 8 d = 3 a = -1 \(S_{21} = \frac{51}{2}[2(a) + 50d]\) = 51 [-1 + 25(3)] = 51 (74) = 3774

Find the sum of the first (i) 11 terms of the A.P : 2,6,10,14, ....(ii) 13 terms of the A.P : -6,0,6,12,....(iii) 51 terms of the A.P. whose second term is 2 and fourth term is 8.

Answer»

(i)

a = 2, d = 6 – 2 = 4

S₁₁=\(\frac{11}{2}\) [2(a) + 10d]

= \(\frac{11}{2}\)[2(2) + 10(4)]

= 11 [2 + 20]

= 242

(ii)

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

S₁₃= \(\frac{13}{2}\)[2(a) + 12d]

= 13 [-6 + 6(6)]

= 13 [-6 + 36]

= 13 (30) = 390

(iii)

a₂= 2 a + d = 2 (i)

a₄= 8 a + 3d = 8

2 – d + 3d = 8

2 + 2d = 8

d = 3

a = -1

\(S_{21} = \frac{51}{2}[2(a) + 50d]\)

= 51 [-1 + 25(3)]

= 51 (74)

= 3774