Geometric Sequences

Geometric Sequence: A sequence in which terms are found by multiplying a preceding term by a nonzero constant.


Recursive Formula: U_n=run-1
The recursive formula, for geometric sequences, uses the terms, preceding the term you are trying to find, to find the term you need to find.

Explicit Formula: U_n = U₁r^{(n - 1)}

The Explicit formula, for geometric sequences, allows you to find a term within the sequence based on the position in the sequence the term is in.


EXAMPLE:
In a geometric sequence, if U₃=125 and U₅=3125
a. What is the constant ratio?
U₅/ U₃ = 3125/125
U₁r²/U₁r⁴ = 3125/125 = √r² = √25
r = 5
b. Find U₈.

U₈ = (5)5⁽⁸⁻¹⁾ = 390,625