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Question

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

A
64
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B
66
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C
226
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D
228
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Solution

The correct option is A 64

It is also given that a3=12 and a50=106
Using formula an=a+(n1)d to find nth term of AP, we get
a50=a+(501)d106=a+49d(1)
a3=a+(31)d12=a+2d(2)

Subtracting (1) and (2), we get,
47d=94
d=2

Substituting d in (2), we get,
a+2(2)=12
a=124=8

The 29th term is,
a29=a+(291)d=8+28(2)=8+56=64


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