Question

The $4th$ and $10th$ terms of an $A.P$. are $13$ and $25$ respectively.

Find its $\left(i\right)$ first term $\left(ii\right)$ common difference $\left(iii\right)17th$ term.

Answer 1

$T_4=a+3d=13\dots \left(1\right)$

$T_{10}=a+9d=25\dots \left(2\right)$

Subtract (1) from (2)

$a+9d-a-3d=6d=25–13=12$

So $d=2$

From $\left(1\right),a=13-6=7$

i) The first term is $7$

ii) The common difference is $2$

iii) the ${17}_{th}$ term = $a+16d=7+32=39$.