What is the definition of a geometric sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence.
An arithmetic sequence is a sequence in which each term of the sequence is obtained by adding a pre-determined value, called the common difference, to the preceding term. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying a pre-determined value, called the common ratio, to the preceding term.

Organized Videos:
✅ Sequences
✅Sequences | Learn About
✅Determine The First Five Terms of The Arithmetic Sequence
✅How to Write The Formula for a Arithmetic Sequence
✅Find the nth Term of an Arithmetic Sequence
✅Find the First Five Terms of a Geometric Sequence
✅How to Write The Formula for a Geometric Sequence
✅Find the nth Term of a Geometric Sequence
✅How to Determine Arithmetic or Geometric Sequence
✅Find the First Five Terms of a Sequence
✅How to Write The Formula for a Sequence
✅Find the nth Term of a Sequence
✅How to Simplify Factorials
✅Recursive Sequences
✅Prove the Sum by Induction
✅Find the Given Term of Binomial Expansion
✅Binomial Expansion | Learn About
✅How to Expand a Binomial

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[toddjacobs]

Mr. McLogan,

I am in geometric sequences right now and a problem in the text discusses a ball that bounces up 1/3 of the fallen height distance.  So, if the ball is dropped at 2 meters, it will bounce up:

2(1/3) = 2/3 meters.

Then it gives the geometric sequence formula, which I understand, for the nth bounce as:

h sub n  =  2/3(1/3)^n-1  =  2(1/3)^n

What I am having trouble understanding is how they go from the first equals sign to the second.  I understand the geometric sequence formula given in the text as:

a sub n  =  a * r^n-1, where a is the first term and r is the ratio.

I’m sure it is some easy first semester algebra, however, my brain is beyond overload right now.  Can you explain how the text went from the first to the second equals sign?  (...and yes, I know typing formulas can get ugly!)

Thank you VERY much for your time.

Todd