Question

What is the explicit rule for this geometric sequence?

a1=23;an=9⋅an−1



an=9⋅(23)n

an=23⋅9n

an=9⋅(23)n−1

an=23⋅9n−1

Answer 1

I took it, and assuming I'm reading your question right, it's D: an=2/3*9^n-1

Answer 2

The Information about Geometric sequence is:

`a_(1)=23 , a_(n)=9* a_(n-1)`

→nth term of sequence = 9× (n-1) th term

Also , Common Ratio of a Geometric Sequence =
`\frac{\text{Second term }}{\text{First term}}`

`(a_(n))/(a_(n-1))= \text{Common ratio}}=9\\a_(n)= a_(1)* r ^(n-1)\\\\a_(n)=23* 9^(n-1)`

Option 4 :
`a_(n)= 23 * 9^(n-1)` is true.