How do you say that having any confusion he said wouldn’t be able to consist of all the new stages
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.
9514 1404 393
Answer:
21.8 cm
Step-by-step explanation:
A useful way to write the Law of Sines relation when solving for side lengths is ...
a/sin(A) = b/sin(B)
Then the solution for 'a' is found by multiplying by sin(A):
a = sin(A)(b/sin(B)) = b·sin(A)/sin(B)
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We need to know the angle A. Its value is ...
A = 180° -75° -31.8° = 73.2°
Then the desired length is ...
a = (22 cm)sin(73.2°)/sin(75°) ≈ (22 cm)(0.9573/0.9659)
a ≈ 21.8 cm
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I like to use the longest side and largest angle in the equation when those are available. That is why I chose 75° and 22 cm.
