This is a geometric progression. Therefore you must multiply or divide a number by the number before it to arrive at the next number.

We must first find the ratio between each number.

To start, take the second number and divide the first number yielding \(\displaystyle \frac{9}{3}=3\)

Then take the third number and divide the second number which results in \(\displaystyle \frac{27}{9}=3\)

If the resulting number is the same you now know the ratio between each number in the sequence and can apply the ratio to each resulting number.

In this case the number is \(\displaystyle 3\).

So we then take the final number and multiply it by 3 we received to get the answer of \(\displaystyle 27*3=81\).

This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number.

We must first find the difference between each number.

To start, take the second number and subtract the first number.

In this case it yields \(\displaystyle 25-18=7\)

Then take the third number and subtract the second number which results with \(\displaystyle 32-25=7\).

If the resulting number is the same you now know the difference between each number in the arithmetic sequence and can apply the difference to each number.

Again the difference is \(\displaystyle 7\).

So we take the final number and add the difference to it resulting with

\(\displaystyle 39+7=46\)

Then we do the same with the answer to get \(\displaystyle 46+7=53\)

The answer is \(\displaystyle 46,53\).

\(\displaystyle 3,-9,27,-81. . .\) is a geometric progression. Therefore you must multiply or divide a number by the number before it to arrive at the next number.

We must first find the ratio between each number.

To start, take the second number and divide the first number yielding \(\displaystyle \frac{-9}{3}=-3\)

Then take the third number and divide the second number which results in \(\displaystyle \frac{27}{-9}=-3\)

If the resulting number is the same you now know the ratio between each number in the sequence and can apply the ratio to each resulting number.

In this case the number is \(\displaystyle -3\).

So we then take the final number and multiply it by the ratio we received to get the answer of \(\displaystyle -81*-3=243\).

The formula for the number of diagonals in a figure is:

\(\displaystyle \frac{n(n-3)}{2}\)

where \(\displaystyle n\) is the number of sides in the figure.

A pentagon is a five-sided figure, so we plug 5 in for \(\displaystyle n\).

\(\displaystyle \frac{5\cdot (5-3)}{2}=\frac{5\cdot 2}{2}=\frac{10}{2}=5\)

There are 5 diagonals in a pentagon.

The least common multiple is the smallest number that both of the numbers multiply to.

For example, for 2 and 6 it would be 6 because \(\displaystyle 2\times 3=6\)and \(\displaystyle 1\times 6=6\). For 2 and 5 it would be 10 because \(\displaystyle 2\times 5=10\) and \(\displaystyle 5\times 2=10\). For 3 and 8 it would be 24.

Multiply the numbers in the sequence 1,2,3,4 to find their multiples.

So for 15 the multiples are:  \(\displaystyle 15,30,45,60,75,90,105,120,135,150\).

And for 25 the multiples are: \(\displaystyle 25,50,75,100,125,150\).

The least common multiple is \(\displaystyle 75\).

A yard equals 3 feet.

Multiplying an odd and an even number together always results in an even number.

In two years, each person will be 2 years older.  Since there are 3 of them, their ages will be \(\displaystyle 3\times2\) years more, so we add 6 to the original total of 29

If Sarah borrowed 48 books and returned half of them, she now has

\(\displaystyle \frac{48}{2}=24\ books\)

If she then borrowed 9 more, she added 9 to the 24 she had so now she has 33.

If Elaine wants to give 2 slices of pizza to 14 children, then she needs \(\displaystyle 2 * 14\) slices of pizza or 28 slices. 28 slices divided by the number of slice per pizza (8) will give you how many pizzas she needs.

\(\displaystyle 28\div 8 = 3.5\).  

In order to ensure she has enough pizza, she needs to round up so she needs to order 4 pizzas.