# 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 Sₙ = 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 n^{th} term of an AP, l = aₙ = a + (n - 1)d

350 = 17 + (n - 1) 9

333 = (n - 1) 9

(n - 1) = 37

n = 38

Sum of n terms of AP,

Sₙ = n/2 [a + l ]

S₃₈_{ }= 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.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 5

**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

**Summary:**

The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, the number of terms and the sum is n = 38 and s = 6973 respectively.

**☛ Related Questions:**

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- Show that a1, a2,... , an , ...form an AP where an is defined as below (i) an = 3 + 4n (ii) an = 9 - 5n. Also find the sum of the first 15 terms in each case.

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