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Question

The 10th term of an AP is 52 and 16th term is 82. Find the 32nd term and the general term.

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Solution

Let a be the first term and d be the common difference of the given A.P. Let the A.P. be a1, a2, a3..... an.....

It is given that

a10 = 52 and a16 = 82

a+(101)d=52 and a+(161)d=82

a+9d=52 .... (i)

and,

a+15d=82 .... (ii)

Subtracting equation (ii) from equation (i), we get

6d=30

d=5

Putting d=5 in equation (i), we get

a+45=52

a=7

a32=a+(321)d=7+31×5=162

and,

an=a+(n1)d=7(n1)×5=5n+2.

Hence a32=162 and an=5n+2.


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