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anonymous

  • one year ago

Find the next three terms of the sequence –8, 24, –72, 216, . . . A) 648, –1944, 5832 B) 248, –616, 248 C) –648, 1944, –5832 D) 216, –648, 1944

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  1. anonymous
    • one year ago
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    Okay. This is probably an awful way to teach this, but this is how I learned. –8, 24, –72, 216, . . . What I would do is I would first divide 24 and -8 You would get -3. Then try it. -8 x -3 = 24 24 x -3 = -72 Do you understand?

  2. anonymous
    • one year ago
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    Yeah so like the number is -3 and -8*-3 = 24 and 24*-3 = -72 and -72*-3= 216 and so on.. @elite.weeaboo

  3. anonymous
    • one year ago
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    Correct (:

  4. anonymous
    • one year ago
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    216*-3= -648, -648*-3= 1944, 1944*-3= -5832

  5. anonymous
    • one year ago
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    the answer is C

  6. anonymous
    • one year ago
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    I would think so.

  7. anonymous
    • one year ago
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    Wait until idku is done typing. I could be wrong.

  8. idku
    • one year ago
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    Oh, no it is correct, i was just going to make a definitional [ost.

  9. idku
    • one year ago
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    just a brief post about the definitions: A sequence that follows such a pattern (multiplying a term times some number to find the next term), is called a "geometric sequence". This number -3, is the number by which you multiply to find the next term - and it is called "common ratio" (denoted by letter r). So you can say in your case "r=-3" \(a_1\) is a notation for the first term \(a_2\) is a notation for the second term \(a_3\) is a notation for the third term so on..... \(a_n\) is a notation for some \(\rm n\)th term So in a geometric sequence (like yours) you should see that: \(a_1 \times r = a_2\) agree? \(a_2 \times r = a_3\) or \(a_1 \times r \times r ~~= a_1 \times r^2= a_3\) agree? \(a_3 \times r = a_4\) or \(a_1 \times r \times r \times r~~= a_1 \times r^3= a_4\) and thus.... \(a_1 \times r^{n-1} = a_n \)

  10. idku
    • one year ago
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    So if you wanted to find 1000th term of your sequence, you would go: \(a_1 \times r^{n-1} = a_n \) \(a_1 \times r^{1000-1} = a_{1000} \) your first term is -8, so: \((-8) \times r^{1000-1} = a_{1000} \) your common ratio is -3: \((-8) \times (-3)^{1000-1} = a_{1000} \) \(\color{blue}{(-8) \times (-3)^{999} = a_{1000}} \)

  11. anonymous
    • one year ago
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    OH. Cool.

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