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Question
Which term of the A.P. 84, 80, 76, ... is 248?
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 84, 80, 76
`a_n = 0`
a = 84
Now
Common difference (d) = `a_1 - a`
= 80 - 84
= -4
Thus using the above-mentioned formula
`a_n = a + (n -1)d`
0 = 84 + (n -1)(-4)
0 = 84 - 4n + 4
4n = 88
On further simplifying, we get,
`n = 88/4`
n = 22
Thus n = 22
Therefore 84 is the 22nd term of the given A.P
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