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प्रश्न
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
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उत्तर
In the given problem, we need to find the 12th term from the end for the given A.P.
3, 5, 7, 9, ... 201
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) = 3
Last term (an) = 201
Common difference (d) = 5 - 3
=2
Now as we know
`a_n = a + (n - 1)d`
So for the last term
201 = 3 + (n - 1)2
201 = 3 + 2n - 2
201 = 1 + 2n
201 -1 = 2n
Furthur simplifying
200 = 2n
`n = 200/2`
n = 100
So, the 12th term from the end means the 89th term from the beginning.
So, for the 89th term (n = 89)
`a_89 = 3 + (89 - 1)2`
= 3 + (88)2
= 3 + 176
= 179
Therefore the 12th term from the end of the given A.P is 179
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