This week, I focused on geometric sequences.

Geometric sequences share similar characteristics to arithmetic sequences. For one, geometric sequences are patterns, just like our arithmetic sequences from last week! Arithmetic sequences have common differences, such as this one: “5, 10, 15, 20, 25, 30…” You can tell the pattern here is that 5 is being added for every new term!

Geometric sequences, however, have common ratios. Like so: “2, 4, 8, 16, 32, 64…” You should be able to see a pattern here. What’s the pattern? The terms are being multiplied by 2 each time! This is very different from our arithmetic sequence, where numbers were being added as the pattern was continuing. The ratio is determined like so: tn/(tn-1)=r.

The ratio is a very important number. It’s as important to geometric sequences as the common difference, d, is to arithmetic sequences, so get used to finding it!

There are a number of ways that you can utilize the common ratio, r. Say, you wanna find the 9th term in our geometric sequence here. Looks something like this:

t1*r^(n-1) = t9

2*2^(9-1) = t9

2*2^8 = t9

2*256 = t9

512 = t9

The general formula for geometric sequences is t1*r(n-1)=tn