SOLUTION: The second and fifth terms of a geometric series are -15 and 405 respectively. What are the first term and the common ratio in the series? What is the sum of the first 9 terms of t

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Question 673220: The second and fifth terms of a geometric series are -15 and 405 respectively. What are the first term and the common ratio in the series? What is the sum of the first 9 terms of the series?
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

The second and fifth terms of a geometric series are -15 and 405 respectively. 

 a%5B2%5D+=+a%5B1%5D%28r%29%5E1+=+-15  r = -15%2Fa%5B1%5D

 a%5B5%5D+=+a%5B1%5D%28-15%2Fa%5B1%5D%29%5E4+=+405 ⇒  %28-15%29%5E4%2F405+=+a%5B1%5D+=+5  and r  = -3

S%5Bn%5D+=+5%28%281-%28-3%29%5En%29%2F%281-%28-3%29%29%29

S%5B9%5D+=+5%28%281-%28-3%29%5E9%29%2F%284%29%29%29= 24605