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 5.2

Page No:106

Questions No:8

# An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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Here, a₃ = 12 and a_50 = 106. To find : a_29

Given that: a₃ = a + (3 – 1)d = 12

⇒ a + 2d = 12

⇒ a = 12 – 2d . . .(1)

and a_50 = 106

⇒ a + 49d = 106

Putting the value of a from equation (1), we get

12 – 2d + 49d = 106

⇒ 47d = 94 ⇒ d = 2

putting the value of d in equation (1), we get

a = 12 – 2(2) = 8

Therefore, a₂₉ = a + 28d = 8 + 28(2) = 64

Hence, the 29th term of the AP is 64.