Question

18. Let Sbe the sum of the first n terms
of an AP. If S2n = 3n + 14n?, then what
is the common difference?​

Answer 1

The common difference (d) is "7".

Step-by-step explanation:

Let a, d be the first term and common difference respectively.

Given,

$S_{2n}$ = 3n + 14$n^{2}$

Put n = 1, 2, 3, ....

∴  = 3 × 1 + 14

⇒ $S_{2(1)}$  = 3 × 1 + 14 × 1

⇒ $S_{2}$ = 17

⇒ $S_{2}$  = {2a + (2 - 1)d} = 17

⇒ 2a + d =17   ....(1)

and

∴ $S_{4}$ = 3 × 2 + 14

⇒ $S_{4}$ = 3 × 2 + 14 × 4 = 6 + 56 = 62

⇒ $S_{4}$ = 62

⇒ ·{2a + (4 - 1)d} = 62

⇒ 2·{2a + 3d} = 62

⇒ 2a + 3d = 31

⇒ (2a + d) + 2d = 31

⇒ 17 + 2d = 31 [Using equation (1)]

⇒  2d = 31  - 17 = 14

⇒  d = 7

Hence, the common difference(d) is "7".

See ink- https://brainly.in/question/13673876#