# 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 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 = 5
- Last term, l = 45
- Sum of n terms, Sₙ = 400

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

400 = n/2 (5 + 45)

400 = n/2 × 50

n = 16

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

l = aₙ = a + (n -1) d

45 = 5 + (16 -1) d

40 = 15d

d = 40/15

d = 8/3

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

**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

**Summary:**

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.

**☛ Related Questions:**

- 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?
- Find the sum of the first 22 terms of an AP in which d = 7 and 22nd term is 149.
- Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
- If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

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