Reflect the following points over the x-axis. (-5, -3) (-2,-6) (-4,-8)

Mathematics

1 answer:

viktelen [127]3 years ago

8 0

Reflect over x-axis rule: (x,y) -> (x,-y)

(-5,3) --> (-5,-3)

(-2,-6) --> (-2,6)

(-4,-8) --> (-4,8)

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

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$a_n=5 \ for \ n=1 \\
a_n=-10 \ for \ n=2 \\
a_n=20 \ for \ n=3$

You can see it's a geometric sequence because the ratio is constant ( $\frac{a_3}{a_2}=\frac{a_2}{a_1}$ ).
The nth term of a geometric sequence:
$a_n=a_1 \times r^{n-1}$

$a_1=5 \\
r=\frac{a_2}{a_1}=\frac{-10}{5}=-2 \\ \\
a_n=5(-2)^{n-1}$

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:
$\sum^{15}_{n=4} 5(-2)^{n-1}$

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