Question

What function forms a geometric sequence when x= 1,2,3,....?

Answer 1

i think the answer is C

Answer 2

the second function is a geometric sequence

the first function is an arithmetic sequence

the third and fourth are constants

For a sequence to be geometric it must have a common ratio r between the terms

the n th term of a geometric sequence is a
`r^(n-1)`

where a is the first term and r the common ratio

f(x) = - 5
`(3)^(x)` is in this form with r = 3

As a check

f(1) = - 5 × 3 = - 15

f(2) = - 5 × 9 = - 45

f(3) = - 5 × 27 = - 135

This is a geometric sequence with r = 3