Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
========================================================
Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
-----------------
To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
The distance traveled by the light in 2 hours is 2.16×10⁹ km.
<h3 /><h3>Distance:</h3>
This is the total length of space between two points covered by an object. Distance has no regard for direction as it is termed a scalar quantity. The S.I unit of distance is meter(m).
To calculate the distance traveled by the light in 2 hours, first, we need to calculate the speed of the light.
Formula:
- S = d/t................. equation 1
Where:
- S = speed
- d = distance travelled
From the question,
Given:
- d = 1.08×10⁹ km
- t = 1 hour
Therefore,
The distance traveled in 2 hours is
- d = 2×1.08×10⁹
- d = 2.16×10⁹ km
Hence, the distance traveled by the light in 2 hours is 2.16×10⁹ km
Learn more about distance here: brainly.com/question/23848540
Answer:
18in^2
Step-by-step explanation:
4,016
4,000
+
16
Which would equal 4,016
