1. Geometric Sequence
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Step-by-step explanation:
Given sequence is:
6, 18, 54, 162,....
Here

(a) Is this an arithmetic or geometric sequence?
We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.
We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

As the common ratio is same, the given sequence is a geometric sequence.
(b) How can you find the next number in the sequence?
Recursive formulas are used to find the next number in sequence using previous term
Recursive formula for a geometric sequence is given by:

In case of given sequence,

So to find the 5th term

(c) Give the rule you would use to find the 20th week.
In order to find the pushups for 20th week, explicit formul for sequence will be used.
The general form of explicit formula is given by:

Putting the values of a_1 and r

Hence,
1. Geometric Sequence
2. 
3. 
Keywords: Geometric sequence, common ratio
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Answer:

Step-by-step explanation:
Given the initial ratio of 3 parts water to 5 parts fruit juice, you can set up a proportion (equivalent ratios) to determine the amount of water needed with just 1 part of fruit juice:

cross multiply: 5x = 3
divide: 5x/5 = 3/5 or x = 3/5
3/5 = 0.6 parts water
118.56. 31.2 x 3.8 = 118.56
Step-by-step explanation:
It looks like you have to draw a figure and then label every side with how long it is.
This first shape is a pentagon because it has 5 sides, and for each side of the pentagon the length would be 3/5 so .6 inches.
The second shape is a square because it has 4 sides, you than would label each side as 1 ft, because when you add them all it equals 4.
The third shape is a triangle with 3 equal sides. When you divide 16.8/3 it shows thag each side of this triangle will be labeled with 5.6 meters.
Thé vertex of the graph of the following function f(x)=x2+8x-2 is (-4,-18).