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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