Can someone please help me find the geometric sequence of
1 answer:
Answer:
Step-by-step explanation:
Step 1. Calculate the common ratio
a₁ = 200
a₂ = 100
a₃ = 40
a₄ = 16
The ratios of consecutive pairs are
a₄/a₃ = 16/40 = 0.4
a₃/a₂ = 40/100 = 0.4
a₂/a₁ = 100/200 = 0.5
I think you have made a typo in your question. The first term should be 250. Then,
a₂/a₁ = 100/250 = 0.4
And all adjacent pairs will have the same common ratio, r = 0.4.
Step 2. Write the formula for the series
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
If a₁ = 250, the formula for the series is
You might be interested in
Answer:
a) To determine the minimum sample size we need to use the formula shown in the picture 1.
E is the margin of error, which is the distance from the limits to the middle (the mean) of the confidence interval. This means that we have to divide the range of the interval by 2 to find this distance.
E = 0.5/2 = 0.25
Now we apply the formula
n = (1.645*0.80/0.25)^2 = 27.7 = 28
The minimum sample size would be 28.
b) To answer the question we are going to make a 90% confidence interval. The formula is:
(μ - E, μ + E)
μ is the mean which is 127. The formula for E is shown in the picture.
E = 0.80*1.645/√8 = 0.47
(126.5, 127.5)
This means that the true mean is going to be contained in this interval 90% of the time. This is why it doesn't seem possible that the population mean is exactly 128.
Answers:
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
====================================================
Explanation:
Here are all the ways to multiply to 18 when using integers only:
- -1*(-18) = 18
- -2*(-9) = 18
- -3*(-6) = 18
- 1*18 = 18
- 2*9 = 18
- 3*6 = 18
Sum each pair of factors to find out a possible value of b.
- -1 + (-18) = -19
- -2 + (-9) = -11
- -3 + (-6) = -9
- 1 + 18 = 19
- 2 + 9 = 11
- 3 + 6 = 9
Therefore, the possible values of b are
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
which are the final answers.
----------------------
An example:
Let's say b = 11. This would mean becomes
It would factor to since it was stated earlier that:
2+9 = 11
2 * 9 = 18
You can use the FOIL rule, distributive property, or the box method to confirm that is a true equation for all real numbers x.
This same idea applies for the other values of b.
----------------------
If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)
Use the FOIL rule to get
The middle term has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).