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[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
f(x) = - 5[tex](3)^{x}[/tex] 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
