Question

find the 20th term from the last term of the ap 3,8,13.....253

Answer 1

a20=a+(n-1)d

     = 3+19*5

    = 98 

20 th term is 98

Answer 2

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
=> 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 ,
= 3 + 31 × 5 = 3 + 155 = 158

hence , 20th term from last = 158