purplemexican
  • purplemexican
can someone explain the geometric series formula? please
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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TrojanPoem
  • TrojanPoem
S = a( R^n- 1) /R-1 a -> first term. R -> a_{n+1} / a_{n} S-> Sum n _> number of terms a_{n} = aR^n the term that n can be found using this formula.
anonymous
  • anonymous
The geometric series is often written as:\[\sum_{n=0}^{\infty}t^n\]
purplemexican
  • purplemexican
so if give 4−12+36−.... what goes where in the formula

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mathmale
  • mathmale
More specifically, if the first term (a) is 4, how do we get from that 4 to the next term, -12? Similarly, if the 2nd term is -12, how do we obtain the 3rd term, 36? We're talking about r, the "common ratio"
purplemexican
  • purplemexican
yea what im trying to figure out is how to get the common ratio so i can determine the sum of the 6th term
purplemexican
  • purplemexican
Find the sum of the first 666 terms in this geometric series: 4 - 12 + 36 - ... the sum would be -728 correct?
purplemexican
  • purplemexican
6th term not 666 term
TrojanPoem
  • TrojanPoem
Common ratio : R = a_{n+1} / a_{n}
TrojanPoem
  • TrojanPoem
-12/4 = -3 -12 * -3 = 36 (verified)
mathmale
  • mathmale
You wanted to know how to find the common ratio. If the first term (a) is 4, how do we get from that 4 to the next term, -12? Similarly, if the 2nd term is -12, how do we obtain the 3rd term, 36? We're talking about r, the "common ratio" The first and second terms are 4 and -12, respectively. The common ratio is -12/4 = ?? We can check this by doing a similar operation on the 2nd and 3rd terms: The second and third terms are -12 and 36. Dividing 36 by -12, we get what? This result is your common ratio, r.

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