## anonymous one year ago 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:)

1. mathstudent55

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

2. anonymous

yes!

3. 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 $$4 \cdot 3^1=$$

4. anonymous

12

5. 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 =

6. anonymous

144?

7. mathstudent55

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

8. 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.

9. anonymous

36

10. mathstudent55

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

11. anonymous

ok so the next is 4 x 3^3

12. 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.

13. mathstudent55

Yes, that's it.

14. anonymous

108 is what I got

15. anonymous

so a.

16. mathstudent55

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

17. anonymous

ok

18. anonymous

would you mind helping with one more

19. mathstudent55

No. Wait.

20. anonymous

ok

21. mathstudent55

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

22. anonymous

oh its c

23. mathstudent55

Correct!

24. anonymous

ok thank you

25. anonymous

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

26. anonymous

I dont get the - 1 part

27. anonymous

ohh minus 1

28. anonymous

nvm

29. mathstudent55

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

30. anonymous

yes

31. mathstudent55

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

32. anonymous

yes

33. 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

34. anonymous

512

35. 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.

36. mathstudent55

You calculated it correctly, but I made a mistake.

37. mathstudent55

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

38. anonymous

ok

39. mathstudent55

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

40. anonymous

ok its c

41. anonymous

128

42. anonymous

yay I got 100 gtg

43. mathstudent55

Yes, C is correct, 128.