Question

If the $5th$ and $8th$ term of an AP are $6$ and $15$ respectively, find the $19th$ term

• A. $48$
• B. $54$
• C. $19$
• D. $57$

Answer 1

The correct option is A $48$

Given: $a_5=6$ and $a_8=15$

$\Rightarrow$ $a_n=a+(n-1)d$

$\Rightarrow$ $6=a+(5-1)d$

$\Rightarrow$ $6=a+4d$

$\Rightarrow$ $a+4d=6$ ----- ( 1 )

Now,

$\Rightarrow$ $a_8=a+(8-1)d$

$\Rightarrow$ $15=a+7d$

$\Rightarrow$ $a+7d=15$ ----- ( 2 )

Subtracting equation ( 1 ) from ( 2 ) we get,

$\Rightarrow$ $3d=9$

$\Rightarrow$ $d=3$

Substituting value of $d$ in equation ( 1 ) we get,

$\Rightarrow$ $a+\left(4\right)\left(3\right)=6$

$\Rightarrow$ $a+12=6$

$\Rightarrow$ $a=-6$

Now,

$\Rightarrow$ $a_{19}=a+(19-1)d$

$\Rightarrow$ $a_{19}=-6+18\left(3\right)$

$\Rightarrow$ $a_{19}=-6+54$

$\therefore$ $a_{19}=48$