Question

Find the number of terms in the A.P., $100,96,92,........,12$

Answer 1

We know that the formula for the nth term is $t_n=a+(n-1)d$, where $a$ is the first term, $d$ is the common difference.

It is given that the nth term is $t_n=12$, the first term is $a=100$ and the difference $d=96-100=-4$, therefore,

$t_n=a+(n-1)d\Rightarrow 12=100+(n-1)(-4)\Rightarrow 12=100-4n+4\Rightarrow 12=104-4n\Rightarrow -4n=12-104\Rightarrow -4n=-92\Rightarrow n=\frac{92}{4}=23$

Hence, the number of terms are $23$.