Question

For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.

Answer 1

Let a and d represent the first term and common difference, respectively.

So, a = – 8, a_n = 55 , and S_n = 235

We know, `S_n = n/2 (a + a_n)`

⇒ 235 = `n/2(-8 + 55)`

⇒ 470 = n(47)

⇒ n = 10

Now, a_n = a + (n – 1)d

⇒ 55 = – 8 + (10 – 1)d

⇒ 55 + 8 = 9d

⇒ 63 = 9d

⇒ d = 7

Hence, the number of terms is 10 and common difference is 7.