let S be the sum of the first n terms of an AP.S2n=3n+14n2 ,then what is the common diffrence?
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The common difference(d) is "7".
Step-by-step explanation:
Let a, d be the first term and common difference respectively.
Given,
= 3n + 14
Put n = 1, 2, 3, ....
∴ = 3 × 1 + 14
⇒ = 3 × 1 + 14 × 1
⇒ = 17
⇒ ·{2a + (2 - 1)d} = 17
⇒ 2a + d =17 ....(1)
and
∴ = 3 × 2 + 14
⇒ = 3 × 2 + 14 × 4 = 6 + 56 = 62
⇒ = 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".
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