Question

If the $7th$ term of an A.P. is $15$ and $13th$ term is $27$, find the $nth$ term.

Answer 1

$a_7=15=a+6d$....(1)

$a_{13}=27=a+12d$...(2)

Subtracting $e{q}^n$ (1) & (2)

$a+6d=15$

$a+12d=27$

__________________

$-6d=-12$

$d=2$

Putting in eq${}^n$ (1), we get ;

$a+6d=15$

$a+6\left(2\right)=15$

$a+12=15$

$a=3$

$\therefore n^{th}$ term $=a_n=a+(n-1)d$

$3+(n-1)2$

$\Rightarrow 3+2n-2$

Solution, $a_n\Rightarrow 1+2n$