If the eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by . . .

Question : If 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.

Doubt by Ananya

Solution :
a₈=a₂/2 (Given)
2a₈=a₂
2(a+7d) = a+d [∵ a_n=a+(n-1)d]
2a+14d=a+d
2a-a+14d-d=0
a+13d=0 ----------(1)

a₁₁-(a₄)/3 = 1
a+10d - (a+3d)/3 = 1
[3a+30d-a-3d]/3 = 1
2a+27d = 3 -----------(2)

Solving eq (1) and (2) by elimination method

[a+13d = 0]×2
2a+27d = 3

2a+26d = 0
2a+27d = 3
-   -          -
----------------
0  -    d = -3
----------------

-d=-3
 d=3

putting this value of d in eq (1)
a+13(3)=0
a+39=0
a=-39

Now, 
a_n=a+(n-1)d
a₁₅=a+(15-1)d
a₁₅=-39+14(3)
a₁₅=-39+42
a₁₅=3