an ap consists of 50 terms of which 3rd term is 12 and the last term is 106 find the 29th term
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an ap consists of 50 terms of which 3rd term is 12 and the last term is 106 find the 29th term
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Answer:
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We know that
an=a+(n-1)d
Given 3rd term is 12
a3= a+(3-1)d
12= a+2d
a=12-2d .........(1)
Given last term is 106
Last term =50th term=106
a50= a+(50-1)d
106= a+49d
a=106-49d .........(2)
From (1) and (2), we get
12-2d=106-49d
-2d+49d=106-12
47d=94
d=2
putting the value of d in (1 )
a=12-2(2)
a=12-4
a=8
Now we need to find 29th term
We know that
an=a+(n-1)d
Putting values
a29=8+(29-1)2
=8+56
=64
Hence, 29th term is 64