Answer:
Step-by-step explanation:
-3
Answer:
-273
Step-by-step explanation:
find the common difference:
d = 7 - 11 = - 4
a_1 = 11
a_72 = (72 - 1)* (-4) + a_1
a_72 = (71)* (-4) + 11
a_72 = -273
Answer:
- f[1] = 3
- f[n] = 2·f[n-1] +4
- 108
Step-by-step explanation:
We observe that first differences of the given numbers are ...
10 -3 = 7
24 -10 = 14
52 -24 = 28
That is, each difference is 2× the previous one. This suggests an exponential relation that has a base of 2.
We notice that doubling a term doesn't give the next term, but gives a value that is 4 less than the next term. So, we can get the next term by doubling the previous one and adding 4.
Then our recursive relation is ...
f[1] = 3 . . . . the first term
f[n] = 2×f[n-1] +4 . . . . double the previous term and add 4
The next term is 2·52 +4 = 108.
Assuming that the sides of the box are square (having 90° angles on all four corners), then it should be relatively easy for us to find the length of the box, given the perimeter and the length of one side.
We know the length of all sides combined is 42 inches, and that the length of one side is 9 inches. With a rectangular prism, the length of one side is the same as the length of the opposite side, so there are two sides that measure 9 inches.
All we need to do to find the measure of both the other sides' lengths is subtract the known lengths from the total length.
9 + 9 = 18
42 - 18 = 24
So the rest of the side lengths added together is 24 inches.
There are two sides left, so all we have to do is divide by 2 to find the length of the box.
24 / 2 = 12
The length of Kate's jewelry box is 12 inches.
Hope that helped =)
