Question

Which sequence is modeled by the graph below?

coordinate plane showing the points 2, 9; 3, 3; and 4, 1
A) an = one third(27)n − 1
B) an = 27(one third)n − 1
C) an = 1(−3)n − 1
D) an = 3(one half)n − 1

Answer 1

Answer:

an=27(one third) - 1

thanks

Answer 2

Answer:

The correct answer is:

                Option: B

   $B.\ a_n=27(\dfrac{1}{3})^{n-1}$

Step-by-step explanation:

We are given that the graph passes through (2,9) , (3,3) and (4,1)

Now, the function which models the graph is given by:

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

when n=2 we have:

$a_2=27(\dfrac{1}{3})^{2-1}\\\\i.e.\\\\a_2=27(\dfrac{1}{3})^1\\\\i.e.\\\\a_2=9$

when n=3 we have:

$a_3=27(\dfrac{1}{3})^{3-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^2\\\\i.e.\\\\a_3=3$

when n=4 we have:

$a_3=27(\dfrac{1}{3})^{4-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^3\\\\i.e.\\\\a_4=1$