Question

Find the 10^th term from the end of the A.P. 8, 10, 12, ..., 126.

Answer 1

In the given problem, we need to find the 10^th term from the end for the given A.P.

We have the A.P as 8, 10, 12 …126

Here, to find the 10^th 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 (a_n) = 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 10^th term from the end of the given A.P is 108