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3 years ago

13

Let me know the answer plz

1 answer:

Cloud [144]3 years ago

8 0

Answer: Option G

$a_6 = -2048$

Step-by-step explanation:

The geometric series have the following form:

$a_n = a_1 (r) ^ {n-1}$

Where $a_1$ is the first term of the sequence and r is the common radius.

In this case we know that

$a_1 = -2\\\\r = 4$

So:

$a_n = -2(4) ^ {n-1}$

To find the sixth term $a_6$ , substitute $n = 6$ in the equation.

$a_6 = -2 (4) ^ {6-1}\\\\a_6 = -2 (4) ^ 5\\\\a_6 = -2048$

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xxTIMURxx [149]

The missing coordinates of the parallelogram is (m + h, n).

Solution:

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Solve using mid-point formula:

$$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )$

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$$=\left( \frac{m+h}{2}, \frac{n+0}{2}\right )$

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<u>To find the missing coordinate:</u>

Let the missing coordinates by x and y.

Here $x_1=0, y_1=0, x_2=x, y_2=y$

$$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )$

Now equate the x-coordinate.

$$ \frac{m+h}{2}=\frac{x}{2}$

Multiply by 2 on both sides of the equation, we get

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x = m + h

Now equate the y-coordinate.

$$\frac{n}{2} = \frac{y}{2}$

Multiply by 2 on both sides of the equation, we get

n = y

y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

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