anonymous
  • anonymous
Find S7 for the geometric series 2 + -6 + 18 + -54 +… i got 1450?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Almost. What is the common ratio?
anonymous
  • anonymous
3
anonymous
  • anonymous
So close. What about the change in sign every term?

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More answers

anonymous
  • anonymous
-3
anonymous
  • anonymous
That's it.
anonymous
  • anonymous
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?
anonymous
  • anonymous
-4374?
anonymous
  • anonymous
Not quite. \[-54 \times -3 \times -3 \times -3 = ?\]
anonymous
  • anonymous
I got 1458... that's not right though.
anonymous
  • anonymous
It sure is.
anonymous
  • anonymous
Why do you think it's incorrect?
anonymous
  • anonymous
the answer choices are 162 -486 1094 -4374
anonymous
  • anonymous
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?
anonymous
  • anonymous
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.
anonymous
  • anonymous
That will give you the correct answer.
anonymous
  • anonymous
\[S_7 = 2\left( \frac{ 1-\left( -3 \right) ^7}{ 1-\left( -3 \right) } \right) = ?\]

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