Answer
The general formula for this exponential sequence is
[tex]y=9(2)^{x-1}[/tex]
x = 1, 2, 3, 4....
Explanation
We can see that this sequence has each of the next term being 2 multiplied by the previous term.
9, 18, 36, 72, 144....
So, we will treat the exponential sequence as a geometric sequence.
The general formula for the nth term of a geometric sequence is
aₙ = arⁿ⁻¹
[tex]a_n=ar^{n-1}[/tex]
where
aₙ = nth term
a = first term = 9
r = common ratio = (Second term)/(First term) = (Third term)/(Second term) etc
r = (18/9) = (36/18) = (72/36) = (144/72) = 2
n = number of terms
So, the general formula for this exponential sequence will be
aₙ = arⁿ⁻¹
a = 9
r = 2
aₙ = 9 (2)ⁿ⁻¹
[tex]a_n=ar^{n-1}[/tex]
So, if we replace the nth term with the xth term, we can say
y = 9 (2)ˣ⁻¹
Hope this Helps!!!
