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.