The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term.

Explanation

Let the first term and common difference of A.P. be a and d respectively.
Given that `T_(8)=(1)/(2)T_(2)`
`rArr 2(a|7d)=a+d rArr a=-13d " " ...(1)`
and `T_(11)-(1)/(3)T_(4)=1 rArr (a+3d)=1`
`rArr 3a+30d-a-3d=3 rArr 2a+27d=3`
`rArr -26d=27d=3 " " ` [from(1)]
`rArr s=3`
From equation (1)
`a=-13xx3=-39`
Now`T_(15)=a+14d=-39+14xx3=3`