Question

1. For sequence A, describe in words a way to produce each new term from the previous term.2. If these sequences continue, which will be greater A(9) or B(9)? Explain or show how you know.

Answer 1

Part 1: Finding the terms of sequence A.

If you compare the terms 1 and 2, you can see that the second term is the previous term multiplied by 4. Also, you can observe the same if you compare terms 2 and 3.

So, to produce each term from the previous term, multiply the previous term by 4.

Part 2: Comparing both sequences.

We already know how to find the terms of sequence A (part 1).

To find the terms of sequence B, observe the graph and then you can see that a term is its previous term plus 2.

Knowing that you can find the terms of the sequence and compare A(9) and B(9)

Term number A B

4 64 10

5 64*4 = 256 10+2 = 12

6 256*4 = 1024 12+2 = 14

7 1024*4 = 4096 14+2 = 16

8 4096*4 = 16384 16+2 = 18

9 16384*4 = 65536 18+2 = 20

As can be noted, if the sequences continue A(9) will be greater then B(9), since A(9) = 65536 and B(9) = 20.