Question

Find the 20th term from the last term of the AP 3, 8, 13, .....253.

Answer 1

Given series is 3, 8, 13, ...... 253
here, first term , a = 3
common difference , d = 5
Let us find total number of terms at first.
use $\bf{T_n=a+(n-1)d}$
=> 253 = 3 + (n - 1)5
=> 250 = 5(n - 1)
=> n - 1 = 50
=> n = 51
so, there are 51 terms in given series.
now we know, mth term from last =last term - mth term + 1
so, 20th term from last = 51 - 20 + 1 = 32
hence, 20th from last = 32th term from first

use , $\bf{T_{32}=a+(32-1)d}$
= 3 + 31 × 5 = 3 + 155 = 158

hence , 20th term from last = 158

Answer 2

Solution :

We have, l = Last term = 253

and,

               d = Common difference = 8 - 3 = 5

∴ 20th term from the end = l - (20 - 1)d

                                           = l - 19d

                                           = 253 - 19 × 5

                                           = 253 - 95 = 158