Question

If $a_3=15,S_{10}=125$, find $d$ and $a_{10}$

Answer 1

Given: $a_3=15,S_{10}=125$
$\Rightarrow a_3=15$
$\Rightarrow a+2d=15$
$\Rightarrow a=15-2d$ ------------- (1)
Now,
$\Rightarrow s_{10}=125$
$\Rightarrow 125=\frac{10}{2}[2a+(n-1\left)d\right]$
$\Rightarrow 125=5\left[2\right(15-2d)+(10-1\left)d\right]$ [Using $eq.\left(1\right)$]
$\Rightarrow \frac{125}{5}=30-4d+9d$
​$\Rightarrow 25=30+5d$
$\Rightarrow 25-30=5d$
​$\Rightarrow -5=5d$
​$\Rightarrow d=-1$
From (1), we have

$\Rightarrow a=15-2\times -1=17$

Hence, $a_{10}=a+9d=17-9=8$