## anonymous one year ago 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

1. 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?

2. Michele_Laino

hint: $\Large q = \sqrt[9]{{\frac{{{a_{10}}}}{{{a_1}}}}} = \sqrt[9]{{\frac{{59049}}{3}}} = ...?$

3. 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

4. anonymous

note that once you find $$q$$ you don't have to compute $$q^n$$ again and you can just determine the sum using $$S=\frac{a_{10}-a_1}{q-1}$$

5. condor34