Question

The first term of an A.P is $5$, the common difference is $3$ and the last term is $80$, find the number of terms.

Answer 1

Given that the first term $a=5$

the common difference $d=3$ and

the last term is $80$

Let the last term be the $n^{th}$ term

We know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=80$

$⟹5+(n-1)\ast \left(3\right)=80$

$⟹5-3+3n=80$

$⟹2+3n=80$

$⟹3n=80-2$

$⟹n=\frac{78}{3}$

$⟹n=26$

Therefore, the number of terms in the given sequence is $26$