Question

Use a recursive function for the geometric sequence 2, −8, 32, −128, … to represent the 9th term.

A. f(9) = f(1) + −4(8)
B. f(9) = f(8) + −4(8)
C. f(9) = f(1) • (−4)8
D. f(9) = f(8) • (−4)

Answer 1

Option D.

Explanation:

The given geometric sequence is

2, −8, 32, −128, …

Here first term is 2 and common ratio is

`\text{Common ratio}=(-8)/(2)=-4`

The recursive formula for a GP is

`f(n)=f(n-1)\cdot r`

where, r is common ratio.

We need to find the recursive function to represent the 9th term.

Substitute n=9 and r=-4 in the above function.

`f(9)=f(9-1)\cdot (-4)`

`f(9)=f(8)\cdot (-4)`

Therefore, the correct option is D.

Answer 2

D. f(9) = f(8) • (−4)

Explanation:

The common ratio for this geometric sequence is -8/2 = -4, so the 9th term is -4 times the 8th term:

f(9) = -4·f(8) . . . . . matches choice D