Question

The second term of an AP is $(x–y)$ and the$5^{th}$ term is $(x+y)$, then its first term is

• A.
• B.
• C.
• D.

Answer 1

Correct option is D.

Since, second erm of the AP is $(x–y)$, therefore,

$\Rightarrow a_2=a+(2-1)d=x-y$

$\Rightarrow a+d=x-y$

$\Rightarrow a=x-y-d$...(i)

Also, the fifth term of the AP is $(x+y)$, therefore,

$\Rightarrow a_5=a+(5-1)d=x+y$

$\Rightarrow a+4d=x+y$

$\Rightarrow x-y-d+4d=x+y$ [From (i)]

$\Rightarrow 3d=2y$

$\Rightarrow d=\frac{2y}{3}$

Therefore,

$\Rightarrow a=x-y-\frac{2y}{3}$ [From (i)]

$\Rightarrow a=x-\frac{5y}{3}$