Week 2 – Precalc 11 | Shelby Connelly's Blog

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 “ $t_n$ “, “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 $t_n$ = $t_1$ · $r^{n - 1}$ .

Example: Find $t_{10}$ : 1, 2, 4, 8, 16

$t_{10}$ = ? $t_1$ = 1 r = 2 n = 10

$t_n$ = $t_1$ · $r^{n - 1}$

( $t_{10}$ ) = (1) $(2)^{(10) - 1}$

$t_{10}$ = 1 · $2^9$

$t_{10}$ = 1 · 512

$t_{10}$ = 512

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