Question

The $8$th term of an A.P. is $17$ and the $19$th term is $39$. Find the $25$th term.

Answer 1

Given that: $T_8=17,T_{19}=39,T_{25}=?$
To find $T_{25}$, first we should find $a$ and $d$.
$d=\frac{T_p-T_q}{p-q}$
$d=\frac{T_{19}-T_8}{19-8}=\frac{39-17}{11}=\frac{22}{11}\therefore d=2$
Consider,
$T_8=17$
$a+7d=17$ $[\therefore T_n=a+(n-1\left)d\right]$
$a+7\left(2\right)=17$
$a+14=17$
$\therefore a=3$
To find $T_{25},T_n=a+(n-1)d$
$T_{25}=3+(25-1)2=3+(24\times 2)=3+48$
$\therefore T_{25}=51$