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anonymous

  • one year ago

Find S7 for the geometric series 2 + -6 + 18 + -54 +… i got 1450?

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  1. anonymous
    • one year ago
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    Almost. What is the common ratio?

  2. anonymous
    • one year ago
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    3

  3. anonymous
    • one year ago
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    So close. What about the change in sign every term?

  4. anonymous
    • one year ago
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    -3

  5. anonymous
    • one year ago
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    That's it.

  6. anonymous
    • one year ago
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    Now, four terms are given, and you need the 7th term. So, take the 4th term (-54) and multiply by the common ratio three more times. What do you get?

  7. anonymous
    • one year ago
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    -4374?

  8. anonymous
    • one year ago
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    Not quite. \[-54 \times -3 \times -3 \times -3 = ?\]

  9. anonymous
    • one year ago
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    I got 1458... that's not right though.

  10. anonymous
    • one year ago
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    It sure is.

  11. anonymous
    • one year ago
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    Why do you think it's incorrect?

  12. anonymous
    • one year ago
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    the answer choices are 162 -486 1094 -4374

  13. anonymous
    • one year ago
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    OK. Perhaps it's a notation issue. Perhaps, when the questions asks for S7, what they want is the SUM of the first 7 terms. Could that be it?

  14. anonymous
    • one year ago
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    If so, to calculate the sum of the first n terms of a geometric series, use\[\sum_{i=1}^{n} a_i = a \left( \frac{ 1-r^n }{ 1-r } \right)\]where a is the 1st term, r is the common ratio, and n is the number of terms to be summed.

  15. anonymous
    • one year ago
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    That will give you the correct answer.

  16. anonymous
    • one year ago
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    \[S_7 = 2\left( \frac{ 1-\left( -3 \right) ^7}{ 1-\left( -3 \right) } \right) = ?\]

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