Question

find the 12th term from the end of the A.p.3,8,13,....253

Answer 1

AP of mth term is $\bf\huge a_{m - n + 1}$

AP is 3, 8, 13, ….. ,253

a = 3

d ⇒ 8 - 3 = 5

$\bf\huge a_{m} = 253$

253 = 3 + ( m - 1)5  

253 - 3 = (m - 1)5

250 = (m - 1)5

$\bf\huge\frac{250}{5} = (m - 1)$

m - 1 = 50

m = 51

According to information  

n = 12

12th term from end

$\bf\huge a_{51 - 12 + 1} = a_{40}$

= 3 + 39(5)

= 3 + 195

= 198

Answer 2

Given that,

An AP 3,8,13,....253

To find,

The 12th term from the end.

Solution,

We have, 3,8,13,....253

First term, r = 3

Common difference, d = 5

Last term, l = 253

Let's find number of terms in this AP.

$a_n=a+(n-1)d\\\\253=3+(n-1)5\\\\253=3+5n-5\\\\n=\dfrac{255}{5}\\\\n=51$

To find the 12th term from the end, we need to find the (51−11)th term from starting of A.P i.e. n = 40

So,

$a_{40}=3+(40-1)5\\\\a_{40}=198$

Hence, the 12th term from the end is 198.