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.

Given:

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

To do:

We have to find the number of terms.

Solution:

Let the first term of the A.P. be $a$ and the common difference be $d$.
This implies,

$a=5, d=3$
Let the last term of the A.P. be nth term.

Therefore,

$a_n=a+(n-1)d$

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

$80-5=3n-3$

$3n=75+3$

$3n=78$

$n=\frac{78}{3}$

$n=26$

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

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Updated on: 10-Oct-2022

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