Question

Given the sequence 2, 6, 18, 54, ..., which expression shown would give the fifteenth term?

Answer 1

Every next term appears to be three times the previous term, so the sequence is defined recursively by


`a_n=3a_(n-1)`

and explicitly by


`a_n=3a_(n-1)=3^2a_(n-2)=\cdots=3^(n-1)a_1`

Given that
`a_1=2`, you have


`a_n=2*3^(n-1)\implies a_(15)=2*3^(14)=9565938`

Answer 2

`a_(15) = 2(3)^(14)`

Explanation:

the sequence 2, 6, 18, 54, ...,

3 is multiplied with first term to get 6

2*3 = 6

6* 3= 18

18 * 3= 54

Each term is multiplied with 3 to get next term

Given sequence is geometric

To get nth term we use formula

`a_n = a_1(r)^(n-1)`

Where 'a1' is the first term

r is the common ratio

n is the number of terms

first term a1= 2

Each term is multiplied with 3 to get next term, so r= 3

now we need to find out the fifteenth term so n= 15

`a_(15) = 2(3)^(15-1)`

`a_(15) = 2(3)^(14)`