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.
Answer:
Rate of change: 4/3
Step-by-step explanation:
Number of sodas/Total cost
pick a number
24/18 = 4/3
<h2>Answer</h2>
8640 square inches
<h2>Explanation</h2>
To solve this, we are going to take advantage of the fact that 1 square foot is equal to 144 square inches so we can create a suitable conversion fraction.
Since we want to convert from square feet from inches, the denominator of our conversion fraction will be square feet so we can cancel those out and get the result in square inches:
There are 8640 square inches in 60 square feet
Answer:
9+5x=t
Step-by-step explanation:
