anonymous
  • anonymous
Find the sum of a 10-term geometric sequence when the first term is 3 and the last term is 59,049 and select the correct answer below. pleeaaassseeee someone help
Mathematics
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anonymous
  • anonymous
Find the sum of a 10-term geometric sequence when the first term is 3 and the last term is 59,049 and select the correct answer below. pleeaaassseeee someone help
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Michele_Laino
  • Michele_Laino
we have to apply the subsequent formula: \[\Large {a_{10}} = {a_1}{q^9}\] from which we have: \[\Large q = \sqrt[9]{{\frac{{{a_{10}}}}{{{a_1}}}}}\] where q is the constant of the geometric sequence. What is the value of q?
Michele_Laino
  • Michele_Laino
hint: \[\Large q = \sqrt[9]{{\frac{{{a_{10}}}}{{{a_1}}}}} = \sqrt[9]{{\frac{{59049}}{3}}} = ...?\]
Michele_Laino
  • Michele_Laino
the requested sum S, is given by the subsequent formula: \[\Large S = {a_1}\frac{{1 - {q^9}}}{{1 - q}} = ...?\] where a_1=3, namely is the first term of your geometric sequence

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anonymous
  • anonymous
note that once you find \(q\) you don't have to compute \(q^n\) again and you can just determine the sum using $$S=\frac{a_{10}-a_1}{q-1}$$
Condor34
  • Condor34
so whats the answer?

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