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

Solution:

Given AP is: 3, 8, 13, …, 253

Common difference, d= 5.

Therefore, we can write the given AP in reverse order as;

253, 248, 243, …, 13, 8, 5

Now for the new AP,

First term, a = 253

and common difference, d = 248 − 253 = −5

n = 20

Using the nth-term formula, we get;

a₂₀ = a + (20 − 1) d

a₂₀ = 253 + (19)(−5)

a₂₀ = 253 − 95 = 158

Therefore, the 20^th term from the last term of AP 3, 8, 13, …, 253 is 158.