Question

Find the common difference of an A. P. whose first term is $\frac{1}{2}$ and the 8th term is $\frac{17}{6}$. Also write its 4th term.

Answer 1

Given $a=\frac{1}{2}$ $a_8=\frac{17}{6}$

now $a_8=a+7d$

$\frac{17}{6}=\frac{1}{2}+7d$

$\frac{17}{6}-\frac{1}{2}=7d$

$7d=\frac{17-3}{6}=\frac{14}{6}$

$[d=\frac{1}{3}]$ where d is common difference

now $a_4=a+3d=\frac{1}{2}+3\times \frac{1}{3}=1+\frac{1}{2}$

$[a_4=\frac{3}{2}]$