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