This week in Precalculus 11, we learned about geometric sequences.

**Geometric sequence**: a list of terms in which each term is multiplied by a common ratio to equal the next term

**Term**: a number (represented by ““, “n” being the term’s place in the geometric sequence)

**Common ratio**: a common number multiplied by each term to equal the next term (represented by “r”)

Example: 1, 2, 4, 8, 16 r = 2

To find the value of a term in a geometric sequence, we use the formula = · .

Example: Find : 1, 2, 4, 8, 16

= ? = 1 r = 2 n = 10

= ·

() = (1)

= 1 ·

= 1 · 512

= 512

This method of finding the value of terms in an geometric sequence is faster than extending the list.