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kirill [66]
3 years ago
13

Use sigma notation to represent the following series for the first 10 terms. 3+ (-6) +12+(-24)

Mathematics
1 answer:
pshichka [43]3 years ago
5 0

Answer: - 1023

Step-by-step explanation:

Given

Sequence is 3+(-6)+12+(-24)...

The following sequence is a geometric series with common ratio r=-2

first term a=3

Sum=\sum _{i=1}^{n}ar^{n-1}=\dfrac{a(1-r^n)}{1-r}

Sum=\sum _{i=1}^{n}3(-2)^{n-1}=\dfrac{3(1-(2)^10)}{1+2}

Sum=\sum _{i=1}^{n}3(-2)^{n-1}=-1023

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nevsk [136]

Answer:

Answer of 17 is ㏒(x^{2}+15x), Answer of 33 is x = 8 , Answer of 35 is x = ㏒10/㏒2 , Answer of 37 is  x = -㏒12/㏒8 and Answer of 39 is x = 5

Step-by-step explanation:

17. ㏒x + ㏒(x+15)

     Using property ㏒a + ㏒b = ㏒a×b

     ∴ ㏒x + ㏒(x+15)

        ㏒x×(x+15)

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      Using property 2^a = 2^b

      Then a = b

     ∴x-5 = 3

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      The answer is x = 8

35. 2^x = 10

    Taking log on both sides gives

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37. 8^-x = 12

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      x = -㏒12/㏒8

    The answer is  x = -㏒12/㏒8

39. 5(2^3 × x) = 8

      5(8×x) = 8

      x = 5

    The answer is x=5

 

5 0
3 years ago
A group of friends was working on a student film. They spent $330 on costumes, which was 55% of their total budget. What was the
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Answer:

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Divide both sides by 55

x = 33,000/55

x = 600

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