Which term of the AP – 2, - 7, - 12, … will be - 77? Find the sum of this AP upto the term - 77.

Given, AP – 2, - 7, - 12, …

Let the nth term of an AP is - 77.

Then, first term, a = - 2

common difference, d = - 7 – (2) = - 7 + 2 = - 5.

Let nth term of an AP is - 77

a_n = a + (n - 1)d

- 77 = - 2 + (n - 1) (- 5)

- 75 = (n - 1) (- 5)

15 = n - 1

n = 16

so 16^th term of AP is - 77

S₁₆ is the sum of AP upto the term - 77 .i.e. 16^th term

As, S_n = (a + a_n) [ as last term is given]

= (- 2 - 77)

= 8 (- 79) = - 632

So 16^th term is - 77 and sum upto 16^th term is - 632