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

an=27(one third) - 1

thanks

Answer 2

The correct answer is:

Option: B

`B.\ a_n=27((1)/(3))^(n-1)`

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((1)/(3))^(n-1)`

when n=2 we have:

`a_2=27((1)/(3))^(2-1)\\\\i.e.\\\\a_2=27((1)/(3))^1\\\\i.e.\\\\a_2=9`

when n=3 we have:

`a_3=27((1)/(3))^(3-1)\\\\i.e.\\\\a_3=27((1)/(3))^2\\\\i.e.\\\\a_3=3`

when n=4 we have:

`a_3=27((1)/(3))^(4-1)\\\\i.e.\\\\a_3=27((1)/(3))^3\\\\i.e.\\\\a_4=1`