True Or False

Find x so that x, X +2, X'+3 are the first three terms of a geometric sequence. Then find the 5" term of the

velikii [3]

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.

So, our first term is x.

Then our second term will be our first term multiplied by the common ratio r. So:

$x+2=xr$

And our third term will be our first term multiplied by the common ratio r twice. Therefore:

$x+3=xr^2$

Solve for x. From the second term, we can divide both sides by x:

$\displaystyle r=\frac{x+2}{x}$

Substitute this into the third equation:

$\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2$

Square:

$\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)$

Simplify:

$\displaystyle x+3=\frac{(x+2)^2}{x}$

We can multiply both sides by x:

$x(x+3)=(x+2)^2$

Expand:

$x^2+3x=x^2+4x+4$

Isolate the x:

$-x=4$

Hence, our first term is:

$x=-4$

Then our common ratio r is:

$\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}$

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.

So, our fifth term is -1/4.

4 0

3 years ago

60 minutes is 20% of ? minute s

Hatshy [7]

60 minutes is 20% of 300 minutes

3 0

3 years ago

Read 2 more answers

Which expression represents, 8 times the difference of two numbers?

tiny-mole [99]

Answer:

C, the difference is subtraction so 8 times the difference of two numbers is C

4 0

3 years ago

Read 2 more answers

Please help me figure out the median.

atroni [7]

What you would do is start crossing the highest and lowest values off on both sides of the chart until you had one or two remaining.
Once that is done, you'll be able to determine the median.

The median in this case is 2.

Hope this helps!

8 0

3 years ago

Suppose that Paolo and Sharon are the only consumers of ice cream cones in a particular market. The following table shows their

Rudiy27

Suppose that Paolo and Sharon are the only consumers of ice cream cones in a particular market. The following table shows their monthly demand schedules: Price Paolo’s Quantity Demanded Sharon’s Quantity Demanded (Dollars per cone) (Cones) (Cones) 1 8 16 2 5 12 3 3 8 4 1 6 5 0 4 On the following graph, plot Paolo’s demand for ice cream cones using the green points (triangle symbol). Next, plot Sharon’s demand for ice cream cones using the purple points (diamond symbol). Finally, plot the market demand for ice cream cones using the blue points (circle symbol). Note: Line segments will automatically connect the points. Remember to plot from left to right. Paolo’s Demand Sharon’s Demand Market Demand 0 4 8 12 16 20 24 6 5 4 3 2 1 0 PRICE (Dollars per cone) QUANTITY (Cones)

4 0

2 years ago