Question

Which term of the A.P. –2, –7, –12,..... will be –77? Find the sum of this A.P. upto the term –77.

Answer 1

Given: AP: –2, –7, –12,.....

First term a = –2, common difference d = –7 – (–2) = –5.

Step-wise calculation:

1. Find n such that T_n = –77: 

T_n = a + (n – 1)d – 77 

= –2 + (n – 1)(–5) – 77 + 2 

= (n – 1)(–5) – 75 

= –5(n – 1) 

n – 1 = 15 

⇒ n = 16

2. Sum up to the 16^th term (S_n):

`S_n = n/2 [2a + (n - 1)d]`

`S_16 = 16/2 [2(-2) + (16 - 1)(-5)]`

= 8[–4 + 15(–5)] 

= 8[–4 – 75] 

= 8(–79)

= –632

The term –77 is the 16^th term of the AP and the sum of the AP up to –77 is –632.