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pishuonlain [190]
3 years ago
13

what is the sum of a 7-term geometric series if the first term is -11, the last term is -45,056, and the common ratio is -4?

Mathematics
2 answers:
11Alexandr11 [23.1K]3 years ago
5 0
Sn=(a1)((1-r^n)/(1-r))
=(-11)(1-(-4)^7)/(1-(-4))
=(-11)(1-(-16384))/5)
=(-11)(3277)
=-36047
zaharov [31]3 years ago
4 0

Answer:

The sum of a 7-term geometric series = -36047

Step-by-step explanation:

We have 7-term geometric series if the first term is -11, the last term is -45,056, and the common ratio is -4.

So the GP is

        -11, 44, -176,704,-2816,11264,-45056

Adding these terms we will get

      Sum = -36047

Using equation:

 We have

                  s_n=\frac{a(r^n-1)}{r-1}

                  a = -11, r = -4 and n= 7

 Substituting

                 s_7=\frac{-11((-4)^7-1)}{-4-1}=-36047

The sum of a 7-term geometric series = -36047

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Answer:

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Step-by-step explanation:

We are given the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1

We need to find average rate of change.

The formula used to find average rate of change is : Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}

We have b=-1 and a=-11

Finding g(b) = g(-1)

g(x)=x^2+10x+18\\Putting \ x=-1\\g(-1)=(-1)^2+10(-1)+18\\g(-1)=1-10+18\\g(-1)=9

Finding g(a) = g(-11)

g(x)=x^2+10x+18\\Putting \ x=-11\\g(-11)=(-11)^2+10(-11)+18\\g(-1)=121-110+18\\g(-1)=29

Finding average rate of change

Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{9-29}{-1-(-11)}\\Average \ rate \ of \ change=\frac{-10}{-1+11}\\Average \ rate \ of \ change=\frac{-10}{10}\\Average \ rate \ of \ change=-1

So, the average rate of change of the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1 is -1

5 0
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Step-by-step explanation:

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Step-by-step explanation:

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