Question

If a.p consist of 50 term of which 3rd term is 12 and last term is 106 find 29th term

Answer 1

Given,
a3=12
a+(n-1)d=12
a+(3-1)d=12
a=12-2d.
a=12-4
a=8
Now,
For 29th term, n=29
= 8+(29-1)2
=8+56
=64
a29=64.

Answer 2

Hii Mohini,



a+ 2d= 12...(1)
a+ 49d= 106..(2)
from (1) we get,
a= 12-2d..(3)
Putting the value of a in (2)
a +49d= 106
(12-2d)+49d= 106
49d-2d+12= 106
47d= 106-12
47d= 94
d= 94/47
d= 2
putting the value of d ,
a= 12-2d
a= 12-2×2
a=12-4
a= 8..
Therefore,
29th term of the AP=
= a+28d = 8+28×2= 8+56= 64
Hence,
29th term of the AP is 64

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