# Class 10 Maths Sample Paper 2019 | Q24

#### Arithmetic Progressions

This 2019 CBSE class 10 Maths 4 mark question is from Arithmetic Progressions. An easy 4 mark question in CBSE class 10 sample question paper. Concept tested: nth term of an arithmetic progression.

Question 24: An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

## NCERT Solution to Class 10 Maths

#### With Videos

Step 1: Compute common difference and first term
Data given : a3 = 12 and a50 = 106
an = a + (n – 1)d
3rd term, a3 = a + 2d = 12 ------ (1)
50th term, a50 = a + 49d = 106 ------ (2)
Subtract equation (1) from (2)
a + 49d = 106
-(a + 2d = 12)
47d = 94 or d = 2
Substitute d = 2 in (1)
a + 2(2) = 12
a = 8

Step 2: Compute a29
a = 8 and d = 2
29th term, a29 = a + 28d = 8 + 28(2) = 64

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