Question

The first term of an AP is $5$, common difference is $3$ and the last term is $80$. Find the number of terms.

Answer 1

Step 1. Given:

First term of AP $a=5$,

Common difference $d=3$,

Last term $l=80$

Step 2. Find the number of terms by using the general term of AP:

We have to consider the total number of must be $n.$

We know that the general term of AP is $l=a+(n-1)d$.

$$\begin{gathered} \Rightarrow 80=5+(n-1)3 \\ \Rightarrow 75=(n-1)3 \\ \Rightarrow 25=(n-1) \\ \Rightarrow n=26 \end{gathered}$$

Hence, the number of terms of given AP is 26.