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.
1/4x^2 = -1/2x + 2.....multiply everything by 4
x^2 = -2x + 8
x^2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x + 4 = 0
x = -4
x - 2 = 0
x = 2
solutions are : x = -4 or x = 2
Option D
<u>Answer:
</u>
y = 
is the equation representing proportional relationship.
<u>
Solution:
</u>
For the proportional relationship, for all values of x, 
must be a constant value.
Let’s check option A.
Divide both the sides by x.
For x = 1,
For x = 2,
So is different for x = 1 and x = 2.
So option A do not represent proportional relationship.
Similarly for option B and C also there is constant term in the equation.
So option B and C will also have different values of for two values of x.
For option D
So for all value of x in above case y/x will be 1/3 .hence D is correct option , that is y = (1/3)x is the equation represents proportional relationship.
The smaller number=x
the larger number=10x
we can suggest this equation:
10x-x=81
9x=81
x=81/9=9
The smaller number is 9
The larger number is : 10x=10(9)=90
Answer: the larger number is 90.
