Geometric Sequences

Question

Given: a1=4, a2=−5 and ai=ai−2−3ai−1−3.
Find the next four terms in the sequence. How would I go about solving this?

Answer 1

I am assuming that you mean a_{i =} a_i-2 - 3a_i-1 - 3, if i ≥ 3

 

a₃ = a₁ - 3a₂ - 3 = 4 - 3(-5) - 3 = 16

 

a₄ = a₂ - 3a₃ - 3 = -5 -3(16) - 3 = -56

 

a₅ = a₃ - 3a₄ - 3 = 16 - 3(-56) - 3 = 181

 

a₆ = a₄ - 3a₅ - 3 = -56 - 3(181) - 3 = -602

 

By the way, the sequence generated by the given recursive formula is NOT geometric.  

 

Answer 2

For a geometric sequence, the consecutive terms must have a common ratio with each other.  The formula for geometric sequence is

 

a_n = a₁r^{n - 1}

 

where:

a_n = nth term

a₁ = first term

r = common ratio

n = term sequence