Question

In an AP, given a$=7$, $a_{13}=35$, find d and $S_{13}$.

Answer 1

$a=7,a_{13}=35$

$a_{13}=a+(13-1)d$

$35=7+12d$

$28=12d$

$d=28/12=7/3$

$s_{13}=\frac{13}{2}[2a+(13-1\left)\frac{7}{3}\right]$

$s_{13}=\frac{13}{2}[14+(12\left)\frac{7}{3}\right]$

$s_{13}=\frac{13}{2}[14+28]$

$s_{13}=13\times 21$

$s_{13}=273$