Question

The fifth term of an AP is 25 and the ninth term is 37. Find the 13${}^{th}$ of the A.P.

• A. -2
• B. 2
• C. 3
• D. -3

Answer 1

The correct option is C 3

Let the first term be a, the common difference be d .
Then the $n^{th}$ term
$a_n=a+(n-1)d$
$\Rightarrow a_5=a+4d$ and
$\Rightarrow a_9=a+8d$
Given $a_5=25$ and $a_9=37$

$a+4d=25$ ...(i)
$a+8d=37$ ...(ii)

Subtracting (i) from (ii), we get
$a+8d-a-4d=37-25$
$⟹4d=12$
$⟹d=3$

Substitute the value of d in (i).
$\Rightarrow a+12=25$
$\Rightarrow a=13$
13${}^{th}$ of the A.P = a +12d
$=13+12\times 3$
$=13+36=49$