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Question
Find the 10th term from the end of the A.P. 8, 10, 12, ..., 126.
Solution
In the given problem, we need to find the 10th term from the end for the given A.P.
We have the A.P as 8, 10, 12 …126
Here, to find the 10th 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) = 8
Last term (an) = 126
Common difference (d) = 10 - 8 = 2
Now, as we know,
`a_n = a + (n -1)d`
So for the last term
126 = 8 + (n -1)2
126 = 8 + 2n - 2
156 = 6 + 2n
126 - 6 = 2n
Further simplifying,
120 = 2n
n = 120/2
n = 60
So the 10th tern from the end means the 51 st term from the beginning.
so for the 51 st term (n = 51)
`a_51 = 8 +(51 - 1)2`
= 8 + (50)2
= 108
Therefore the 10th term from the end of the given A.P is 108
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