Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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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.
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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
-6 < x (less than or equal to) 8
Answer:
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Step-by-step explanation:
Answer: Find the greatest common factor, and put in parentheses outside of the expression
Step-by-step explanation:
The greatest common factor is the largest number that all terms are divisible by. Here is an example: 4x+8y+12 In this example the greatest common factor is 4. So, first we divide the expression by 4 and put it in parentheses, giving us (x+2y+3). However, (x+2y+3) does not equal 4x+8y+12. We need to put the 4 we divided by in front of the parentheses, giving us 4(x+2y+3), which does equal 4x+8y+12. Hope this helps
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