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

**Solution:**

Sum of the first n terms of an AP is given by S_{n} = n/2 [2a + (n - 1) d].

Here, a is the first term, d is a common difference and n is the number of terms.

Given,

- First term, a = 17
- Last term, l = 350
- Common difference, d = 9

We know that nth term of AP, l = a_{n} = a + (n - 1)d

350 = 17 + (n - 1) 9

333 = (n - 1) 9

(n - 1) = 37

n = 38

Sum of n terms of AP,

S_{n} = n/2 [a + l]

S_{38 }= 38/2 (17 + 350)

= 19 × 367

= 6973

Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.

**Video Solution:**

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

### Class 10 Maths NCERT Solutions - Chapter 5 Exercise 5.3 Question 6:

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

The number of terms and the sum is n = 38 and s = 6973 respectively.