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

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

Answer»

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

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