Question

A geometric sequence is shown below.

2, – 6, 18, – 54, 162, ...

Part A:
Write a recursive relationship for this sequence. Explain how you determined your answer.

Part B:
Write an explicit formula for this sequence.

Answer 1

To find the recursive rule u have to find r so first so u have to divide the 2nd term by the 1st term to get r so it would be -6 divided by 2 which equals -3 then u have to plug in r with -3 so this is how it’s done so f(n)= f(n-1)•r then plug in r with -3 so then to find the explicit rule u have to plug in f(1) with your 1st term which is 2 and plug in r with -3 so f(n)= 2•(-3)n-1