# Find the 12th Term from the End of the Following Arithmetic Progressions: 3, 8, 13, ..., 253 - Mathematics

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

3, 8, 13, ..., 253

#### Solution

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

3, 8, 13 …253

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 (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 12th term from the end means the 40th term from the beginning.

So, for the 40th 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.

Concept: nth Term of an AP
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 13.2 | Page 25