Question

In an AP. It is given that S₅ + S₇ = 167 and S₁₀ = 235, then find the AP, where S_n denotes the sum of its first n terms.

Answer 1

Let a be the first term and d be the common difference of thee AP. Then,

S₅ + S₇ = 167

12a + 31 x 5 = 167

\(\Rightarrow\) 12a + 155 = 167

\(\Rightarrow\) 12a = 167 - 155 = 12

\(\Rightarrow\) a = 1

Hence, the AP is 1, 6, 11, 16,…….