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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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