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.
Is the answer 7632? ithink i got it wrong ill check my answer
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There is no simplest form for a decimal. You can only simplify equations and fractions, not decimals. For example, could you simplify 1? I don't think you could. Well, it's the same concept for -3.75.
Hope that answered your question.
Answer:
$24,000
Step-by-step explanation:
1. Find what 20% of 30,000 is.
20% x 30,000 = 6,000
2. The problem says the cost of a new car is 20% greater than a used car. Subtract the 6,000 from 30,000 to get the cost of the used car.
30,000 - 6,000 = 24,000
3. The cost of the used car is $24,000