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# Solution - An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term - CBSE Class 10 - Mathematics

Conceptnth Term of an AP

#### Question

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

#### Solution

Given that,

a3 = 12

a50 = 106

We know that,

an = a + (n − 1) d

a3 = a + (3 − 1) d

12 = a + 2d (I)

Similarly, a50 = a + (50 − 1) d

106 = a + 49d (II)

On subtracting (I) from (II), we obtain

94 = 47d

d = 2

From equation (I), we obtain

12 = a + 2 (2)

a = 12 − 4 = 8

a29 = a + (29 − 1) d

a29 = 8 + (28)2

a29 = 8 + 56 = 64

Therefore, 29th term is 64.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Textbook for Class 10 (with solutions)
Chapter 5: Arithmetic Progressions
Q: 8 | Page no. 106

#### Reference Material

Solution for question: An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term concept: null - nth Term of an AP. For the course CBSE
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