What are the first four terms in the multiplication pattern given by the formula?
4 · 3n
A.
4, 12, 36, 108
B.
7, 21, 63, 189
C.
12, 36, 108, 324
D.
12, 24, 36, 48
WILL MEDAL AND FAN:)

- anonymous

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- mathstudent55

You mean to use the n as an exponent?
If so, do you mean the pattern: \(4 \cdot 3^n\)

- anonymous

yes!

- mathstudent55

You are looking for the first 4 terms.
In these patterns, the way they work, is you let n = 1, then n = 2, then n = 3, and so on.
For each of those values of n, evaluate the expression.
Let's start with n = 1.
What is \(4 \cdot 3^1= \)

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## More answers

- anonymous

12

- mathstudent55

A number raised to the 1 power is the number itself.
So you are correct.
That is the first number in the pattern.
Now let n = 2.
What is 4 * 3^2 =

- anonymous

144?

- mathstudent55

A number raised to the second power, called the square of a number, is the number multiplied by itself.

- mathstudent55

No.
You need to be careful with the order of operations.
You must do the exponent first.
The exponent is only on the 3, not on 4 * 3.
First do 3^2. What do you get?
Then multiply that result by 4.

- anonymous

36

- mathstudent55

Exactly:
\(4 \cdot 3^2 = 4 \cdot (3 \times 3) = 4 \times 9 = 36\)

- anonymous

ok so the next is 4 x 3^3

- mathstudent55

Now you can do the same pattern for n = 3.
The exponent is 3, and you are just raising the 3 to the power 3. Then multiply by 4.

- mathstudent55

Yes, that's it.

- anonymous

108 is what I got

- anonymous

so a.

- mathstudent55

Correct.
Now use n = 4 to do the 4th term.

- anonymous

ok

- anonymous

would you mind helping with one more

- mathstudent55

No. Wait.

- anonymous

ok

- mathstudent55

The answer is not A.
Remember, we have so far 12, 36, 108.
There is only one choice that starts with those numbers.

- anonymous

oh its c

- mathstudent55

Correct!

- anonymous

ok thank you

- anonymous

What is the third term in the pattern with formula 8 · 4n – 1?
A.
64
B.
96
C.
128
D.
512

- anonymous

I dont get the - 1 part

- anonymous

ohh minus 1

- anonymous

nvm

- mathstudent55

Wait. Once again, we first need to understand this.
I am assuming n - 1 is an exponent, right?

- anonymous

yes

- mathstudent55

This:
\(8 \cdot 4^{n - 1} \)

- anonymous

yes

- mathstudent55

Here you only need the 4th term.
The 4th term has n = 4, since we start with n = 1.
Let n be 4. Then the exponent is 4 - 1 = 3

- anonymous

512

- mathstudent55

The given pattern:
\(8 \cdot 4^{n - 1} \)
For n = 4:
\(8 \cdot 4^{4 - 1} = 8 \cdot 4^3 \)
Now calculate 4^3 and multiply by 8.

- mathstudent55

You calculated it correctly, but I made a mistake.

- mathstudent55

You are asked for the third term.
Just do the same but let n = 3, not 4.

- anonymous

ok

- mathstudent55

\(8 \cdot 4^{3 - 1} = 8 \cdot 4^2\)
This is the correct one.

- anonymous

ok its c

- anonymous

128

- anonymous

yay I got 100 gtg

- mathstudent55

Yes, C is correct, 128.

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