If the 4th and 7th terms of a geometric sequence are 75 and 600, what is the first term?
1 answer:
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So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.
Understanding that we know the shadow lengths, we can turn these into a fraction such as so:
4ft/20ft.
Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.
Your fraction for that would look like:
5.5ft/X
Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.
Now we can solve.
4ft/20ft =5.5ft/X
We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:
4x = 110ft
This is a simple one step equation. Divide both sides by 4 to get your answer.
x= 27.5ft.
This means your Utility pole's height is 27.5ft.
Answer:
Step-by-step explanation:
It's an arithmetic sequence.
9 = 11 - 2
7 = 9 - 2
5 = 7 - 2
3 = 5 - 2
A) next three terms: 3 - 2 = 1, 1 - 2 = -1, -1 - 2 = -3
B) Common difference = -2
C) Recursive Function:
D) Explicit Function:
a₁ - first term
d - common difference
Substitute a₁ = 11 and d = -2: