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

1.	Which term of the AP – 2, - 7, - 12, … will be - 77? Find the sum of this AP upto the term - 77.
Answer» 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 = n/2(a + a_n) [ as last term is given] = 16/2 (- 2 - 77) = 8 (- 79) = - 632 So 16^th term is - 77 and sum upto 16^th term is - 632

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

Answer»

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 = n/2(a + a_n) [ as last term is given]

= 16/2 (- 2 - 77)

= 8 (- 79) = - 632

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