Question

Which strategy best explains how to solve this problem?

Answer 1

Answer:

Use objects to model the problem. Is your answer. i had this on my old test

Answer 2

This is a geometric sequence because each term is twice the value of the previous term.  So this is what would be called the common ratio, which in this case is 2.  Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth value, a=initial value, r=common ratio, n=term number

In this case we have r=2 and a=1 so

a(n)=2^(n-1)  so on the sixth week he will run:

a(6)=2^5=32

He will run 32 blocks by the end of the sixth week.

Now if you wanted to know the total amount he runs in the six weeks, you need the sum of the terms and the sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r)  where the variables have the same values so

s(n)=(1-2^n)/(1-2)

s(n)=2^n-1 so 

s(6)=2^6-1

s(6)=64-1

s(6)=63 blocks

So he would run a total of 63 blocks in the six weeks.