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Question
Which term of the A.P. 21, 42, 63, 84, ... is 420?
Solution
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, `a_n = a + (n -1)d`
Here, A.P is 21, 42, 63, 84
`a_n = 420`
a = 21
Now
Common difference (d) = `a_1 - a`
= 42 - 21
= 21
Thus, using the above mentioned formula
`a_n = a + (n -1)d`
`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
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