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Q : 8    An AP consists of \small 50 terms of  which \small 3rd term is \small 12 and the last term is \small 106. Find the \small 29th term.
 

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It is given that
AP consists of \small 50 terms of  which \small 3rd term is \small 12 and the last term is \small 106
Now,
a_3 = 12=a+2d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
And
a_{50} = 106=a+49d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
On solving equation (i) and (ii) we will get 
a= 8 \ \ \ and \ \ \ d = 2
Now,
a_{29} = a+28d=8+28\times 2 = 8 +56 = 64
Therefore, 29th term of given AP is 64

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Gautam harsolia

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