NCERT Solutions for Class 10 Maths Chapter 5

Important NCERT Questions

Arithmetic Progression

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 5.3

Page No:113

Questions No: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.

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Here, a = 5, a_n = 45 and S_n = 400.

The sum of n terms of an AP is given by

S_n = n/2[a + a_n]

⇒ 400 = n/2[5 + 45]

⇒ 400 = 25n

⇒ n = 400/25 = 16

a_n = a + (n – 1)d

⇒ 45 = 5 + (16 – 1)d

⇒ 40 = 15d

⇒ d = 40/15 = 8/3

Hence, the number of term are 16 and the common difference is 8/3.