Which term of the AP: 3, 8, 13, 18, …, is 78?

Given:

Given A.P. is $3, 8, 13, 18 ……$

To do:

We have to find $78$ is which term of the given A.P.

Solution:

Let $78$ be the nth term of the given A.P.

Here,

$a_1=3, a_2=8, a_3=13$

Common difference $d=a_2-a_1=8-3=5$

We know that,

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

Therefore,

$a_{n}=3+(n-1)(5)$

$78=3+n(5)-1(5)$

$78-3=5n-5$

$75+5=5n$

$5n=80$

$n=\frac{80}{5}$

$n=16$

Hence, $78$ is the 16th term of the given A.P.  

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Updated on: 10-Oct-2022

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