Question

The sum of first $7$ terms is $63$ and sum of next of seven terms is $161$ find ${25}^{th}$ terms

Answer 1

$S_7=63$

$\frac{7}{2}[2a+(7-1\left)d\right]=63$

$14a+42d=126$

$a+3d=9$ --- (i)

Sum of next seven term is $161$

$S_{14}-S_7=161$

$\frac{14}{2}[2a+13d]-63=161$

$7(2a+13d)=224$

$a+\frac{13}{2}d=16$ ---- (ii)

on subtracting (i) from (ii)

we get,

$d=2$

from (i)

$a=3$

$a_{25}=a+24d$

$=3+24\times 2=51$