Question

Find the respective terms for the following $APs$
$a_1=5,a_4=9\frac{1}{2}$ find $a_2,a_3$

Answer 1

$a_1=5$ $a_4=9\frac{1}{2}$
$a_1=a=5$ ...........(1)
$a_4=a+3d=5+3d=9\frac{1}{2}$ .......(2)
Equation (1)-(2), gives
$-3d=5-\frac{19}{2}=\frac{10-19}{2}=\frac{-9}{2}$
$\Rightarrow d=\frac{3}{2}$
$\therefore a_2=a+d=5+\frac{3}{2}=\frac{13}{2}$
$\therefore a_3=a+2d=5+2\times \frac{3}{2}=8$
$\therefore a_2=\frac{13}{2},a_3=8$