Math 1 · Unit 9 · Lesson 3 · part 3 of 5
It is an exponential: the ratio is the growth factor
The dots sit on an exponential curve, so a geometric sequence is the exponential family from Unit 7 in...
It is an exponential: the ratio is the growth factor
The dots sit on an exponential curve, so a geometric sequence is the exponential family from Unit 7 in list form.
- 1The common ratio is the growth factor.The r of a geometric sequence is the b of y = a · bx: the number you multiply by each step. Bigger than 1 grows; between 0 and 1 decays.
- 2The terms are dots on the curve.Only whole-number term numbers exist, so plot the dots and leave the curve out, or draw it faintly as a guide.
- 3Watch where the counting starts.Unit 7 started at x = 0, so the exponent was x. A sequence starts at n = 1, so the exponent is n − 1. Same list, different starting number.
Slide the common ratio across 1 and watch the dots switch from shrinking to growing.
| What it is | Function notation | Sequence notation | Say it |
|---|---|---|---|
| the term | f(n) | an | a sub n |
| the previous term | f(n − 1) | an − 1 | a sub n minus 1 |
| the next term | f(n + 1) | an + 1 | a sub n plus 1 |
| the first term | f(1) | a1 | a sub 1 |