Question

Which sequence is modeled by the graph below?

coordinate plane showing the points 2, 1; 3, 3; and 4, 9

an = one third(27)n − 1

an = 27(one third)n − 1

an = one third(3)n − 1

an = 3(one half)n − 1

Answer 1

the answer is C. an = one third (3)n − 1

i just took the test.

Explanation:

Answer 2

`a_n=(1)/(3)\cdot (3)^(n-1)`

C is correct.

Explanation:

We need to choose correct model by the graph which passes through the points (2,1) (3,3) and (4,9)

Option 1:
`a_n=(1)/(3)\cdot (27)^(n-1)`

Put n=2 and to get a₂=1

`a_2=(1)/(3)\cdot (27)^(2-1)`

`a_2=9`

`9\\eq 1`

False

Option 2:
`a_n=27\cdot ((1)/(3))^(n-1)`

Put n=2 and to get a₂=1

`a_2=27\cdot ((1)/(3))^(2-1)`

`a_2=9`

`9\\eq 1`

False

Option 3:
`a_n=(1)/(3)\cdot (3)^(n-1)`

Put n=2 and to get a₂=1

`a_2=(1)/(3)\cdot (3)^(2-1)`

`a_2=1`

`1= 1`

TRUE

Similarly, we will check (3,3) and (4,9)

and we will get true

Hence, The sequence is
`a_n=(1)/(3)\cdot (3)^(n-1)`