Question

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 1, 3, 9, 27, 81,...

Answer 1

a geometric sequence is a bunch of numbers where you can get from a number to the next number by multiplying the previous number by a certain number

might be confusing so here's an example

1,2,4,8,16

each term is multiplied by 2 to get next term, that number that each term is multiplied by is called the common ratio

formula for geometric sequence is

$a_n=a_1(r)^{n-1}$

where $a_n$ is nth term

$a_1$ is first term

r is teh common ratio

n=which term

in our example

1,3, 9, 27, 81

each term is being multiplied by 3 so it is a geometric sequence and thus r=3

also first term is 1 so $a_1=1$

so the formula is $a_n=1(3)^{n-1}$ or in function notation $f(n)=1(3)^{n-1}$

Answer 2

This is a geometric sequence.

from 1-3 one is multiplied by three

from 3-9 three is multiplied by three

from 9-27 nine is multiplied by three

and from 27-81 27 is multiplied by three

Hope this helped!!

|Sophia M|