# The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference

**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 the common difference and n is the number of terms.

Given,

- First term, a = 5
- Last term, l = 45
- Sum up to nth terms, S
_{n}= 400

We know that sum of n terms of AP is given by the formulaS_{n} = n/2 [a + l]

400 = n/2 (5 + 45)

400 = n/2 × 50

n = 16

By using the formula a_{n} = a + (n -1) d, we will find the common difference where a_{n }= l.

l = a_{n} = a + (n -1) d

45 = 5 + (16 -1) d

40 = 15d

d = 40/15

d = 8/3

**Video Solution:**

## The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference

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

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference

The number of terms and the common difference is n = 16 and d = 8/3 if the first term of an AP is 5, the last term is 45 and the sum is 400