Question

Find the common difference in an arithmetic seres, where $S_{15}=322.5$ and the first is $4$.

• A. $1.5$
• B. $2.5$
• C. $3.5$
• D. $4.5$

Answer 1

Answer: (B)

$2.5$

$S_n=\frac{n}{2}[t_1+t_n]$
$\Rightarrow 322.5=\frac{15}{2}[4+t_n]$
$\Rightarrow 322.5=7.5[4+t_n]$
$\Rightarrow 43=4+t_n$
$\Rightarrow t_n=39$

$t_n=a+(n-1)d$
$\Rightarrow 39=4+(15-1)d$
$\Rightarrow 35=14d$
$\Rightarrow d=2.5$