Question

Which formula describes the following geometric sequence? Remember that n represents the term number.2, 6, 18, 54, ...

a. an = 2 · 3n - 1
b. an = 3 · 2n - 1
c. an = 2 + 3(n - 1)
d. an = 3 + 2(n - 1)

Answer 1

Choice A

Explanation:

Answer 2

The given sequence is 2, 6, 18, 54, ...

Notice that this is a geometric sequence because here we have equal common ratio.

So, common ratio :
`r = (a_(2))/(a_(1))`

=
`(6)/(2)`

= 3

The formula for general term of a geometric sequence is,

`a_(n) =a_(1)* r^(n-1)`

Where, first term: a_{1} =2

Next step is to plug in these values in the above equation to get the formula for the given sequence.

`a_(n) =2* 3^(n-1)`

Hence, the correct choice is A.