Determine whether each sequence is geometric? <br>
1) 60,48,36,24,12,…<br>
2) 3,6,12,24,48,…
balandron [24]
Answers:
- Not geometric
- Geometric
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Explanation for problem 1
Divide each term over its previous term.
- term2/term1 = 48/60 = 0.8
- term3/term2 = 36/48 = 0.75
We can stop here. The two results 0.8 and 0.75 do not match up, so we don't have a common ratio. Therefore, this sequence is <u>not</u> geometric. A geometric sequence must have each ratio of adjacent terms to be the same value throughout the list of numbers.
Side note: This sequence is arithmetic because we are subtracting the same amount each time (12) to generate each new term.
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Explanation for problem 2
Like before, we'll divide each term by its previous term.
- term2/term1 = 6/3 = 2
- term3/term2 = 12/6 = 2
- term4/term3 = 24/12 = 2
- term5/term4 = 48/24 = 2
Each ratio found was 2. This is the common ratio and it shows we have a geometric sequence. It indicates that each term is twice that of its previous term. Eg: the jump from 12 to 24 is "times 2".
Answer:
Step-by-step explanation:
Linear equations can have the form y = mx + b
where m is the slope of the line and equals Δy/Δx
and b is the y intercept.
Just for fun, let's choose the first and last sets of data points.
Δy = (275 - 135) = 140
Δx = (5 - 1) = 4
so slope m = 140/4 = 35 and the units on the slope would be $/month
(x-4)(x+6)
x= 4, -6
...........
So, I'm not use to that type of currency, but I can still help you.
The equation would be:
145 + 60(d-1) = 445
Now since it is 60 per day after that, the first day would not be charge, the second would but you would not charge it more.
145 + 60d - 60 = 445
Add like terms
85 + 60d = 445
-85 -85
60d= 360
d= 6
You can even check using a table/ coordinates. x= days, y=money
(1, 145), (2, 205), (3, 265), (4, 325), (5, 385), (6, 445).
