Review question

How do we add the odd-numbered terms of a geometric series? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8617

Suggestion

A geometric series has first term $a$ and common ratio $r$, where $|r|<1$. The sum to infinity of the series is $8$. The sum to infinity of the series obtained by adding all the off-numbered terms (i.e. 1st term + 3rd term + 5th term + …) is $6$. Find the value of $r$.

We know the terms of the series we are given form a geometric series.

What can we say about the series formed by taking the odd-numbered terms instead?