What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?

Answer:26042.Step-by-step explanation:What's the first term of this geometric series?2.What's the common ratio of this geometric series?Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2. [tex]\displaystyle r = \frac{-10}{2} = -5[/tex].What's the sum of this series to the seventh term?The sum of the first n terms of a geometric series is:[tex]\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r}[/tex], where[tex]a_1[/tex] is the first term of the series,[tex]r[/tex] is the common ratio of the series, and[tex]n[/tex] is the number of terms in this series.[tex]\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042[/tex].