# Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22 - Mathematics

Sum

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22

#### Solution

Let a be the first term and d be the common difference of the given A.P. Then,

a2 = 2 and a7 = 22

⇒ a + d = 2 and a + 6d = 22

Solving these two equations, we get

a = – 2 and d = 4.

S_n = \frac { n }{ 2 } [2a + (n – 1) d]

∴ S_30 = \frac { 30 }{ 2 } [2 × (–2) + (30 – 1) × 4]

⇒ 15 (–4 + 116) = 15 × 112

= 1680

Hence, the sum of first 30 terms is 1680

Concept: Sum of First n Terms of an AP
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