Final answer:
A student is inquiring about a finite geometric series with a first term of 2, last term of -6250, and a common ratio of -5. To find the sum of this series, we need to calculate the number of terms and then apply the sum formula for a geometric series.
Step-by-step explanation:
The student is asking about how to find the sum of a finite geometric series that has specific characteristics: it starts with 2, ends with -6250, and has a common ratio of -5. The general formula for the sum of a finite geometric series is S = a(1 - r^n) / (1 - r), where 'S' is the sum of the series, 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms in the series.
First, we need to determine the number of terms in the series. Given that the last term is -6250 and the first term is 2, we can set up the equation 2 * (-5)^(n-1) = -6250 and solve for 'n'. The solution to this equation will give us the number of terms.
Once we have the number of terms, we can apply the sum formula directly to find the total sum of the series. This will involve substituting our values for 'a', 'r', and 'n' into the formula and simplifying to find the sum.