Question

How many terms are there in the A.P. $7,13,19,\dots ,205$ ?

Answer 1

Calculate number of terms in the given A.P.

Given, $7,13,19,\dots ,205$ are in A.P.

$a=7$ and $d=13–7=6$
$a_n=a+(n–1)d$ ……..$\left(i\right)$

$a_n=$Last term $=205$ ………$\left(ii\right)$

Equation $\left(i\right)$ and $\left(ii\right)$, we get,

$\Rightarrow a+(n–1)d=205$

$\Rightarrow 7+(n–1)\left(6\right)=205$

$\Rightarrow 7+6n–6=205$

$\Rightarrow 6n=205–1$

$\Rightarrow n=\frac{204}{6}$

$\Rightarrow n=34$

Hence, number of terms in given A.P. are $34$.