The second term in a geometric series is 10, and the seventh term is 10,240. Find the sum of the first six terms.

Answer:The sum of the first 6 terms is 3,412.5.Step-by-step explanation:The second term of the geometric series is given by:[tex]a_{2}=a_{1}*r[/tex]Where a1 is the first term and r is the common ratio. The seventh term can be written as a function of the second term as follows:[tex]a_{7}=a_{1}*r^{6} \\a_{7}=a_{2}*r^{5} \\10,240 = 10*r^{5}\\r=\sqrt[5]{1024} \\r = 4[/tex]The sum of "n" terms of a geometric series is given by:[tex]a_{1} = \frac{10}{4} = 2.5\\S_{n}=a_{1}(\frac{r^{n}-1 }{r-1})\\S_{6}=2.5(\frac{4^{6}-1 }{4-1})\\S_{6}=3,412.5[/tex]The sum of the first 6 terms is 3,412.5.