Write the sum in sigma notation LaTeX: \displaystyle -15+12-\frac{48}{5}\ldots and then find the sum.

Taking the ratio of the first two terms gives LaTeX: \displaystyle r = \frac{a_2}{a_1}=\frac{12}{-15}=- \frac{4}{5} . Using LaTeX: \displaystyle a_{1} and LaTeX: \displaystyle r to write in sigma notation gives LaTeX: \displaystyle \sum_{n=1}^{\infty}-15\left( - \frac{4}{5} \right)^{n-1} . Using the formula for the sum of an infinite geometric series gives LaTeX: \displaystyle \frac{-15}{1-(- \frac{4}{5})}=- \frac{25}{3}