Question

The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there in the A.P. and what is their sum?

Answer 1

Given: First term, a = 17

Last term, l = 350

common difference, d = 9

We know that,

l = a + (n – 1)d

⇒ 350 = 17 + (n – 1)9

⇒ 333 = (n – 1)9

⇒ 37 = n – 1

⇒ n = 38

So, there are 38 terms in the AP

Now, we have to find the sum of this AP

⇒ S₃₈ = 19 [34 +37×9]

⇒ S₃₈ = 19 [34 + 333]

⇒ S₃₈ = 19 × 367

⇒ S₃₈ = 6973

Hence, the sum of 38 terms is 6973.