Consider the series $5+10+20$5+10+20 ...

Find the sum of the first $12$12 terms.

Find the sum of the first $5$5 terms of the geometric sequence defined by $a=2.187$a=2.187 and $r=1.134$r=1.134.

Give your answer correct to two decimal places.

Find the sum of the first $5$5 terms of the geometric sequence defined by $a=-4.186$a=−4.186 and $r=-2.848$r=−2.848.

Consider the series $1-2+4$1−2+4 ...

Find the sum of the first $11$11 terms.

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.