pre calc question

Question

Find the value of r for this series. 3/4 + 1/4 + 1/12 + 1/36 + 1/108 + . . .

1. 1/4

2. 1/3

3. 3/4

4. 3/4

Answer 1

The letter r in this context stands for ratio, which means the ratio of successive terms in the sequence (here successive means next to one another). In other words, if you start with any term in the sequence, and you multiply by r, you get the next term. Let's write that fact down using the first two terms:

(3/4)*r = (1/4)

You can solve for r here using a little algebra.

We started by assuming that the sequence was geometric, that is, that any successive terms in the sequence will always have the same ratio. Otherwise asking for "r" doesn't make sense. Once you have a value of r, you should check that this ratio is the same between any two terms. So, for example, check using the value of r that you computed, that

(1/12)*r = (1/36)

is a true statement (both sides are the same).