Question

The $11th$ term of AP whose $3rd$ term is $11$ and $8th$ term is $26$ is

• A. $25$
• B. $-2$
• C. $-8$
• D. $35$

Answer 1

The correct option is D $35$

Given, $a_3=11,a_8=26$

if the terms are in $A.P$ then $a_n=a+(n-1)d$

$\Rightarrow a_3=a+2d=11.......\left(1\right)$
$\Rightarrow a_8=a+7d=26.......\left(2\right)$

Subtract equation $\left(2\right)$ from $\left(1\right)$
we get,

$\Rightarrow -5d=-15$
$\therefore d=3$

By putting $d=3$ in equation $\left(1\right)$ we get,
$\Rightarrow a+2\left(3\right)=11$
$\therefore a=5$

$\Rightarrow a_{11}=a+10d$ (by using formula)

$=5+10\left(3\right)$

$=35$
$\therefore$ Option D is correct.