Question

Find the number of terms in the following $A.P.7,13,19,....,205$

Answer 1

Let $a,d$ and $l$ be the first term, common difference and the last term of the A.P. respectively.

Given $a=7,d=13-7=6$ and $l=205$

Since $l=a+(n-1)d$

$\Rightarrow 205=7+(n-1)6$

$\Rightarrow 198=(n-1)6$

$\Rightarrow 33=n-1$

$\Rightarrow n=34$

Hence, there are $34$ terms in the A.P.