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:
y = 5x/2 + 2
Step-by-step explanation:
We know the equation for slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since we have the coordinates of one point on this line and the slope, we can substitute that in and find b first:
y = mx + b
-8 = 5/2(-4) + b
-8 = -10 + b
b = 2
So we can use the slope and this y intercept we found to plug back into the equation:
y = mx + b
y = 5x/2 + 2
Answer:
$2561.50
Step-by-step explanation:
If the account earns simple interest, then the balance at the end of 6 months will be ...
... A = P + Prt . . . . . for principal amount P, interest rate r, time period t
... A = $2350 +2350·0.18·6/12 = $2350 + 211.50
... A = $2561.50
Answer:
The answer is in the attached picture below.
