Question

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:)

Answer 1

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

Answer 2

yes!

Answer 3

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 \(4 \cdot 3^1= \)

Answer 4

12

Answer 5

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 =

Answer 6

144?

Answer 7

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

Answer 8

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.

Answer 9

36

Answer 10

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

Answer 11

ok so the next is 4 x 3^3

Answer 12

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.

Answer 13

Yes, that's it.

Answer 14

108 is what I got

Answer 15

so a.

Answer 16

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

Answer 17

ok

Answer 18

would you mind helping with one more

Answer 19

No. Wait.

Answer 20

ok

Answer 21

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

Answer 22

oh its c

Answer 23

Correct!

Answer 24

ok thank you

Answer 25

What is the third term in the pattern with formula 8 · 4n – 1?

A.
64

B.
96

C.
128

D.
512

Answer 26

I dont get the - 1 part

Answer 27

ohh minus 1

Answer 28

nvm

Answer 29

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

Answer 30

yes

Answer 31

This:

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

Answer 32

yes

Answer 33

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

Answer 34

512

Answer 35

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.

Answer 36

You calculated it correctly, but I made a mistake.

Answer 37

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

Answer 38

ok

Answer 39

\(8 \cdot 4^{3 - 1} = 8 \cdot 4^2\)

This is the correct one.

Answer 40

ok its c

Answer 41

128

Answer 42

yay I got 100 gtg

Answer 43

Yes, C is correct, 128.