Question

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

a_n = `{{:(1,  "if n" = 1),(2,  "if n" = 2),("a"_("n" - 1) + "a"_("n" - 2),  "if n" > 2):}}` 

Answer 1

n = 1, a₁ = 1, n = 2, a₂ = 2
n = 3, a_n = a_n+1 + a_n-2
a₃ = a_{3 – 1} + a_{3 – 2} 
= a₂ + a₁ 
= 2 + 1
= 3

n = 4, a_n = a_n+1 + a_n-2
a₄ = a_{4 – 1} + a_{4 – 2} 
= a₃ + a₂ 
= 3 + 2
= 5

n = 5, a_n = a_n+1 + a_n-2
a₅ = a_{5 – 1} + a_{5 – 2} 
= a₄ + a₃ 
= 5 + 3
= 8

n = 6, a_n = a_n+1 + a_n-2
a₆ = a_{6 – 1} + a_{6 – 2} 
= a₅ + a₄ 
= 8 + 5
= 13
∴ The first six terms are 1, 2, 3, 5, 8, 13