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.
Solution:
Here, a = 5, d = 3, an = 80
Let the number of terms be n.
Then, we have:
$a_{n}=a+(n-1) d$
$\Rightarrow 80=5+(n-1) 3$
$\Rightarrow 75=(n-1) 3$
$\Rightarrow 25=(n-1)$
$\Rightarrow 26=n$
Thus, there are 26 terms in the given A.P.