If the nth term of a progression is (4n - 10) show that it is an AP. Find its

(i) first term,

(ii) common difference, and

(iii) 16th term.

n^th term of the AP is (4n - 10).

For n = 1, we have a₁ = 4 - 10 = - 6

For n = 2, we have a₂ = 8 - 10 = - 2

For n = 3, we have a₃ = 12 - 10 = 2

For n = 4, we have a₄ = 16 - 10 = 6, and so on.

∴ a₄ - a₃ = a₃ - a₂ = a₂ - a₁ = 4 = constant.

∴ the given progression is an AP.

Hence, (i) Its first term = a = - 6

(ii) common difference = 4

(iii) To find :16^th term

∴ a₁₆ = a + (16 - 1)d

⇒ a₁₆ = - 6 + 15 × 4 = 54

∴ 16^th term of the given AP is 54.