Question

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

Answer 1

In the given problem, we are given an A.P and the value of one of its term.

We need to find which term it is (n)

So here we will find the value of n using the formula, ${\displaystyle a_n=a+(n-1)d}$

Here, A.P is 21, 42, 63, 84

${\displaystyle a_n=420}$

a = 21

Now

Common difference (d) = ${\displaystyle a_1-a}$

=  42 - 21

= 21

Thus, using the above mentioned formula

${\displaystyle a_n=a+(n-1)d}$

${\displaystyle 420=21+(n-1)21}$

420 - 21 = 21n - 21

399 + 21 = 21n

`n = 420/21

n = 20

Thus n = 20

Therefore 420 is the 20th term of the given A.P