Question

Find the 12^th term from the end of the following arithmetic progressions:

3, 8, 13, ..., 253

Answer 1

In the given problem, we need to find the 12^th term from the end for the given A.P.

3, 8, 13 …253

Here, to find the 12^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) = 3

`Last term (`a_n`) = 253

Common difference d = 8 - 3

= 5

Now as we know

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

So for the last term

253 = 3 + (n - 1)5

253 = 3 + 5n - 5

253 + 2 = 5n

Further simplifying

255 = 5n

`n = 255/5`

n = 51

So, the 12^th term from the end means the 40^th term from the beginning.

So, for the 40^th term (n = 40)

`a_40 = 3 + (40 - 1)5`

`= 3 + (39)5`

= 3 + 195

= 198

Therefore the 12th term from the end ofthe given A.P.is 198.