Question

Determine the sum of a geometric series whose first term is 12, whose common ratio is -1/4 and whose number of terms is infinite.

Answer 1

A general geometric sequence is of the form \[a_{n}=a\cdot r^{n-1}\] where 'a' is the first term and 'r' is the common ratio. In your case, a=12 and r = -1/4. You can then use the formula \[S=\frac{a}{1-r}\] to find the sum of the infinite series.

So \[S=\frac{12}{1-(-\frac{1}{4})}=\frac{12}{1+\frac{1}{4}}=\frac{12}{\frac{5}{4}}=\frac{48}{5}\]


So the entire infinite series adds up to 48/5