Which term of the A.P. $21, 42, 63, 84, …..$ is $420$?

Given:

Given A.P. is $21, 42, 63, 84, …..$

To do:

We have to find $420$ is which term of the given A.P.

Solution:

Let $420$ be the nth term of the given A.P.

Here,

$a_1=21, a_2=42, a_3=63$

Common difference $d=a_2-a_1=42-21=21$

We know that,

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

Therefore,

$a_{n}=21+(n-1)(21)$

$420=21+n(21)-1(21)$

$420-21=21n-21$

$420=21n$

$n=\frac{420}{21}$

$n=20$

Hence, $420$ is the 20th term of the given A.P.    

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Updated on: 10-Oct-2022

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