Question

1. Use the formula to evaluate the series 2 - 10 + 50 - 250 + ... - 26-Sn =a1(1 - 1)1-rIn the formula for a finite series, a, is the first term, r is the common ratio, and n is the number of terms.-520815,6245208

Answer 1

$\begin{gathered} \text{The series formula given is }S_n=a_1(\frac{1-r^n}{1-r}) \\ \text{The first term a}_1\text{ from the series is }2. \end{gathered}$

The common ratio (r) is obtained by dividing a term by its preceding term.

$\text{common ratio (r) = }\frac{\text{second term }}{\text{first term}}=\frac{10}{-2}=-5$

The number of terms in the series (n) = 6. (from the finite series)

$\begin{gathered} S_6=2(\frac{1-(-5)^6}{1-(-5)}) \\ S_6=\text{ 2(}\frac{1-15625}{1+5}) \\ S_6=2(\frac{-15624}{6})_{} \\ S_6=\text{ }-5208 \end{gathered}$