Question

which statement about geometric sequences are true ?

Answer 1

Step-by-step explanation:

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

an=an−1⋅roran=a1⋅rn−1an=an−1⋅roran=a1⋅rn−1

Example

Write the first five terms of a geometric sequence in which a1=2 and r=3.

We use the first given formula:

a1=2a1=2

a2=2⋅3=6a2=2⋅3=6

a3=6⋅3=18a3=6⋅3=18

a4=18⋅3=54a4=18⋅3=54

a5=54⋅3=162a5=54⋅3=162

Just as with arithmetic series it is possible to find the sum of a geometric series. It is found by using one of the following formulas:

Sn=a1−a1⋅rn1−rorSn=a1(1−rn)1−r