Question

Activity 2
Consider the sequence 2, 6, 18, 54…
Let n = represent the term number in the sequence.
Let A(n) = the value of the nth term of the sequence.
4. What is the common ratio of the sequence?
A (n) = a.r^n= 2.3^n ratio r is= 6/2=18/6 = 3
5. Complete each statement
a. A(1) = 2 = 2 x 3^0
b. A(2) = 6 = 2 x 3 = 2 x 3^1
c. A(3) = 18 = 2 x 3 x 3 = 2 x 3^2
d. A(4) = 54 = 2 x 3 x 3 x 3 = 2 x 3^3
6. What is the relationship between the exponent and the base 3 and the value of n?


What is #6???

Answer 1

For n = 1, exponent = 0
For n = 2, exponent = 1
For n = 3, exponent = 2
For n = 4, exponent = 3
Can you see the relationship between n and the exponent in each step?

Answer 2

It goes up 1 each time??

Answer 3

@mathstudent55

Answer 4

@mathstudent55 are you going to finish helping me??????

Answer 5

Yes, but the question is look at each n and each corresponding exponent. For each value of n, the exponent is 1 less than n, so for each n, the exponent is n-1

Answer 6

ok can you help me with one more??

Answer 7

Complete the statement A(n) = 2 x 3^?

Answer 8

What would this one be? @mathstudent55 ^^

Answer 9

Now since you see that n is matched to exponent n - 1, you get A(n) = 2 x 3^(n -1)

Answer 10

ok thanks