Determine the sum of first 35 terms of an A.P., if the second term is 2 and the seventh term is 22.

Given: a₂ = 2 and a₇ = 22 and n = 35

We know that,

a₂ = a + d = 2 …(i)

and a₇ = a + 6d = 22 …(ii)

Solving the linear equations (i) and (ii), we get

a + d – a – 6d = 2 – 22

⇒ - 5d = -20

⇒ d =4

Putting the value of d in eq. (i), we get

a + 4 = 2

⇒ a = 2 – 4 = -2

Now, we have to find the sum of first 35 terms.

⇒ S₃₅ = 35 [-2 + 34 × 2]

⇒ S₃₅ = 35 [66]

⇒ S₃₅ = 2310