Question

Find the 20^th term from the end of the AP: 3, 8, 13,…, 253.

Answer 1

Given: An A.P: 3, 8, 13, …… , 253 

Here a = a₁ = 3 

d = a₂ – a₁ = 8 – 3 = 5 

a_n = 253, where 253 is the last term 

a_n = a + (n – 1)d 

∴ 253 = 3 + (n – 1)5 

⇒ 253 = 3 + 5n – 5 

⇒ 5n = 253 + 2 

⇒ n = 255/5 = 51 

∴ The 20^th term from the other end would be 

1 + (51 – 20) = 31 + 1 = 32 

∴ a₃₂ = 3 + (32 – 1) × 5 

= 3 + 31 × 5 

= 3 + 155 = 158