Question

Find the $20^{th}$ term from the last term of the AP : 3, 8, 13, …..., 253

Answer 1

Given A.P. is $3, 8, 13, …, 253$
Common difference for this A.P. is $5$.
Therefore, this A.P. can be written in reverse order as:
$253, 248, 243, ..…, 13, 8, 5$
For this A.P.,
$a = 253$
$d = 248 − 253 = −5$
$n = 20$
$a_{20 }= a + (20 − 1) d$
$a_{20 }= 253 + (19) (−5)$
$a_{20} = 253 − 95 a = 158$

Therefore, $20^{th}$ term from the last term is $158$.