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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:)

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  1. mathstudent55
    • one year ago
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    You mean to use the n as an exponent? If so, do you mean the pattern: \(4 \cdot 3^n\)

  2. anonymous
    • one year ago
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    yes!

  3. mathstudent55
    • one year ago
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    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
    • one year ago
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    12

  5. mathstudent55
    • one year ago
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    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
    • one year ago
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    144?

  7. mathstudent55
    • one year ago
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    A number raised to the second power, called the square of a number, is the number multiplied by itself.

  8. mathstudent55
    • one year ago
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    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
    • one year ago
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    36

  10. mathstudent55
    • one year ago
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    Exactly: \(4 \cdot 3^2 = 4 \cdot (3 \times 3) = 4 \times 9 = 36\)

  11. anonymous
    • one year ago
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    ok so the next is 4 x 3^3

  12. mathstudent55
    • one year ago
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    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
    • one year ago
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    Yes, that's it.

  14. anonymous
    • one year ago
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    108 is what I got

  15. anonymous
    • one year ago
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    so a.

  16. mathstudent55
    • one year ago
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    Correct. Now use n = 4 to do the 4th term.

  17. anonymous
    • one year ago
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    ok

  18. anonymous
    • one year ago
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    would you mind helping with one more

  19. mathstudent55
    • one year ago
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    No. Wait.

  20. anonymous
    • one year ago
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    ok

  21. mathstudent55
    • one year ago
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    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
    • one year ago
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    oh its c

  23. mathstudent55
    • one year ago
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    Correct!

  24. anonymous
    • one year ago
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    ok thank you

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

  26. anonymous
    • one year ago
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    I dont get the - 1 part

  27. anonymous
    • one year ago
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    ohh minus 1

  28. anonymous
    • one year ago
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    nvm

  29. mathstudent55
    • one year ago
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    Wait. Once again, we first need to understand this. I am assuming n - 1 is an exponent, right?

  30. anonymous
    • one year ago
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    yes

  31. mathstudent55
    • one year ago
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    This: \(8 \cdot 4^{n - 1} \)

  32. anonymous
    • one year ago
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    yes

  33. mathstudent55
    • one year ago
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    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
    • one year ago
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    512

  35. mathstudent55
    • one year ago
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    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
    • one year ago
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    You calculated it correctly, but I made a mistake.

  37. mathstudent55
    • one year ago
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    You are asked for the third term. Just do the same but let n = 3, not 4.

  38. anonymous
    • one year ago
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    ok

  39. mathstudent55
    • one year ago
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    \(8 \cdot 4^{3 - 1} = 8 \cdot 4^2\) This is the correct one.

  40. anonymous
    • one year ago
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    ok its c

  41. anonymous
    • one year ago
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    128

  42. anonymous
    • one year ago
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    yay I got 100 gtg

  43. mathstudent55
    • one year ago
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    Yes, C is correct, 128.

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