Question

Write the first 6 terms of the sequences whose n^th term a_n is given below.

(i) a_n = {(n + 1 if n is odd), (n if n is even)

(ii) a_n = {(1 if n = 1),(2 if n = 2),(a_{n - 1} + a_{n - 2} if n > 2)

(iii) a_n = {(n if n is 1,2 or 3),(a_{n - 1} + a_{n - 2} + a_{n - 3} if n > 3)

Answer 1

(i) a₁ = 1 + 1 = 2 ; a₂ = 2

a₃ = 3 + 1 = 4 ; a₄ = 4 

a₅ = 5 + 1 = 6 ; a₆ = 6 

So, the first 6 terms are 2, 2, 4, 4, 6, 6

(ii) a₁ = 1 ; a₂ = 2, a₃ = 3 

a₄ = a₃ + a₂ + a₁ = 3 + 2 + 1 = 6 ⇒ a₄ = 6 

a₅ = a₄ + a₃ + a₂ = 6 + 3 + 2 = 11 ⇒ a₅ = 11 

a₆ = a₅ + a₄ + a₃ = 11 + 6 + 3 = 20 ⇒ a₆ = 20 

So the first 6 terms are 1, 2, 3, 5, 8, 13.

(iii) a_n = {(n if n is 1,2 or 3),(a_{n - 1} + a_{n - 2} + a_{n - 3} if n > 3)