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.

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