1.

If the 8th term of an AP is 31 and the 15th term is 16 more than the 11th term, find the AP.

Answer»

Let a be the first term and d be the common difference of the AP.

General term of an A.P.

⇒ an​=a+(n−1)d

We have, a8​=31 and a15​=16+a11​

⟹a+7d=31 and a+14d=16+a+10d

⟹a+7d=31 and 4d=16

⟹a+7d=31 and d=4

⟹a+7×4=31

⟹a+28=31

⟹a=3

Hence, the AP is a,a+d,a+2d,a+3d ...

i.e.,3, 7, 11, 15, 19, ...



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