The first term of an A.P. is 5, the common difference is 3 and the last term is 80;

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, = 3, an = 80

Let the number of terms be n.

Then, we have:

$a_{n}=a+(n-1) d$

$\Rightarrow 80=5+(n-1) 3$

$\Rightarrow 75=(n-1) 3$

$\Rightarrow 25=(n-1)$

$\Rightarrow 26=n$

$\Rightarrow 26=n$

Thus, there are 26 terms in the given A.P.