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

Answer:

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

i just took the test.

Step-by-step explanation:

Answer 2

Answer:

$a_n=\dfrac{1}{3}\cdot (3)^{n-1}$

C is correct.

Step-by-step explanation:

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

Option 1: $a_n=\dfrac{1}{3}\cdot (27)^{n-1}$

Put n=2 and to get a₂=1

$a_2=\dfrac{1}{3}\cdot (27)^{2-1}$

$a_2=9$

$9\neq 1$

False

Option 2: $a_n=27\cdot (\dfrac{1}{3})^{n-1}$

Put n=2 and to get a₂=1

$a_2=27\cdot (\dfrac{1}{3})^{2-1}$

$a_2=9$

$9\neq 1$

False

Option 3: $a_n=\dfrac{1}{3}\cdot (3)^{n-1}$

Put n=2 and to get a₂=1

$a_2=\dfrac{1}{3}\cdot (3)^{2-1}$

$a_2=1$

$1= 1$

TRUE

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

and we will get true

Hence, The sequence is $a_n=\dfrac{1}{3}\cdot (3)^{n-1}$