Question

Suppose the 8 th term of an AP is 31 and the 15 th term is 16 more than the 11 th term. i) Find the AP series. ii) Find the sum of first 15 terms of a series.​

Answer 1

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

Genereal 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, ...