Question

Find the 8^th term from the end of the A.P. 7, 10, 13, ..., 184

Answer 1

In the given problem, we need to find the 8^th term from the end for the given A.P.

We have the A.P as 7, 10, 13 …184

Here, to find the 8^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) = 7

Last term (a_n) = 184

Common difference (d) = 10 - 7 = 3

Now, as we know,

`a_n = a + (n - 1)d`

So, for the last term,

`184 = 7 + (n -1)3`

184 = 7 + 3n - 3

184 = 4 + 3n

184 - 4 = 3n

Further simplifying,

180 = 3n

n = 180

n = 60

So, the 8^th term from the end means the 53^rd term from the beginning.

So, for the 53^rd term (n = 53)

`a_53 = 7 + (53 - 1)3`

= 7 + (52)3

= 7 + 156

= 163

Therefore, the 8^th term from the end of the given A.P. is 163