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Question
Find the 12th term from the end of the following arithmetic progressions:
1, 4, 7, 10, ..., 88
Solution
In the given problem, we need to find the 12th term from the end for the given A.P.
Here, to find the 12th term from the end let us first find the total number of terms. Let us take the total number of terms as n.
So
First term (a) = 1
Last term `(a_n) = 88`
Common difference , `d = 4 -1 = 3`
Now as we know
`a_n = a + (n -1)d`
So for the last term
88 = 1 + (n - 1)3
88 = 1 + 3n - 3
88 = -2 + 3n
88 + 2 = 3n
Furthur simplifying
90 = 3n
`n = 90/3`
n = 30
So the 12 th term from tje end means the 19th term from the beginning.
so for the 19th term (n = 19)
`a_19 = 1 + (19 - 1)3`
`= 1 + (18)3`
= 1 + 54
= 55
Therefore the 12th term from the end of the giving A.P is 55
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