A little confused for this problem, Could use some help

Question

write the first 5 terms of the geometric sequence. Determine common ratio and write the nth term of the sequence as a function n.

a1=80, ak+1=-1/2ak         Note: (k+1) and (k) are bases

Answer 1

Hi Justis,

 

This is an example of a recursive formula for sequences, where each term is defined relative to the previous term.

 

a₁ = 80

a_k+1 = -1/2 a_k

 

If k=1, this tells you that

a₂ = -1/2 a₁

a₂ = -1/2 (80) = -40

 

For k=2, 3, 4, etc you have

a₃ = -1/2 a₂

a₄ = -1/2 a₃

a₅ = -1/2 a₄

a₆ = -1/2 a₅

and so on.

 

You can use these to find a₃, a₄, a₅, etc, one at a time.