Question

For the question below identify each with a coordinating response. Be sure to clearly label each part of your response as part a, part b, and part c.

Answer 1

Given the sequence:

$3,5,9,17,...$

Part A:

You can identify that each term is found by multiplying the previous term by 2 and then subtracting 1 to the Product.

Then, you can write the following equation to represent the pattern:

$a_n=2a_{(n-1)}-1$

Where the previous term is:

$a_{(n-1)}$

And the nth term is:

$a_n$

Parts B and C:

You know the first four terms.

Then, using the equation found in Part A, you can determine that the next five terms are:

$a_5=2a_4-1=2(17)-1=33$

$a_6=2a_5-1=2(33)-1=65$$a_7=2a_6-1=2(65)-1=129$$a_8=2a_7-1=2(129)-1=257$$a_9=2a_8-1=2(257)-1=513$$a_{10}=2a_9-1=2(513)-1=1025$

Hence, the answers are:

Part A: Each term is found by multiplying the previous term by 2 and then subtracting 1 to the Product:

$a_n=2a_{(n-1)}-1$

Part B:

$\begin{gathered} a_5=33 \\ a_6=65 \\ a_7=129 \\ a_8=257 \\ a_9=513 \\ a_{10}=1025 \end{gathered}$

Part C:

$a_5=2a_4-1=2(17)-1=33$

$a_6=2a_5-1=2(33)-1=65$$a_7=2a_6-1=2(65)-1=129$$a_8=2a_7-1=2(129)-1=257$$a_9=2a_8-1=2(257)-1=513$