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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???
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?
It goes up 1 each time??
@mathstudent55 are you going to finish helping me??????
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
ok can you help me with one more??
Complete the statement A(n) = 2 x 3^?
What would this one be? @mathstudent55 ^^
Now since you see that n is matched to exponent n - 1, you get A(n) = 2 x 3^(n -1)