Okay, here we have this:
Considering the provided geometric sequence, we are going to calculate the sum of the first 10 terms, so we obtain the following:
Then we will substitute in the following formula the Sum of the First n Terms of a Geometric Sequence:
Let us remember that in our case "r" is equal to 2, because each term is equal to the previous one multiplied by 2, we have:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex][tex]\begin{gathered} S_{10}=\frac{1.5(1-2^{10})}{1-2} \\ S_{10}=\frac{1.5(1-1024)}{-1} \\ S_{10}=-1.5(-1023) \\ S_{10}=1534.5 \end{gathered}[/tex]Finally we obtain that the sum of the first 10 terms of the geometric sequence is equal to 1534.5.
