what is the 19th term of a geometric sequence where a1=8 and a9=360. Round the common ratio and 19th term to the nearest hundredth.REALLY need help on this one please please.
Accepted Solution
A:
Answer:Step-by-step explanation:[tex]a_{1} = 8\\a_{9} = 360 = a_{1} \cdot r^9 = 8 \cdot r^9\\r = \sqrt[9]{\frac{360}{9} } \cong 1.53[/tex]By the formula of a geometric series:[tex]S_{n} = a \cdot \frac{1-r^n}{1-r} => S_{19} = 8 \cdot \frac{1-1.53^{19}}{1-1.53} = 6091.54[/tex]