Question

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

Answer 1

Given, AP : –2, –7, –12, ….

Let the n^th term of an AP is –77

Then, first term (a) = –2 and

Common difference (d) = –7 – (–2)

= –7 + 2

= –5

∵ n^th term of an AP

T_n = a + (n – 1)d

⇒ –77 = –2 + (n – 1)(-5)

⇒ –75 = –(n – 1) × 5

⇒ (n – 1) = 15

⇒ n = 16

So, the 16^th term of the given AP will be –77

Now, the sum of n terms of an AP is

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

So, sum of 16 terms i.e., upto the term –77

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

= `-[-4 + (16 - 1)(-5)]`

= `8(-4 - 75)`

= `8 xx (-79)`

= ` -632`

Hence, the sum of this AP upto the term –77 is –632.