What are arithmetic and geometric sequences?

An Arithmetic Sequence is such that each term is obtained by adding a constant to the preceding term. This constant is called the Common Difference. Whereas, in a Geometric Sequence each term is obtained by multiply a constant to the preceding term.

What is the formula for arithmetic and geometric sequences?

The explicit formula for an arithmetic sequence is an=a1+d(n−1), where a1 is the initial value and d is the common difference. The explicit formula for a geometric sequence is an=a1(r)n−1, where a1 is the initial value and r is the common ratio.

What are some real world examples of arithmetic and geometric sequences?

Here are a few more examples:

the amount on your savings account ;
the amount of money in your piggy bank if you deposit the same amount each week (a bank account with regular deposits leads you to arithmetico-geometric sequences) ;

How do you sequence a math lesson?

Planning Sequences of Lessons

Decide what success looks like.
Decide what a unit looks like.
Align mathematical tasks to the unit.
Be really specific about the mathematics to be learned.
Group the mathematics into meaningful chunks.
Design tasks for each chunk of mathematics.
Summary:

What is a geometric sequence example?

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms. Example 1: {2,6,18,54,162,486,1458,…}

What is a real life example of geometric sequence?

A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it’s height gets cut down by half. If the ball’s first height is 4 feet, the next time it bounces it’s highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing.

What are geometric sequences used for?

Geometric series are used throughout mathematics. They have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.

Why should teachers plan sequences of lessons?

Teachers planning a sequence of lessons. They start with learning outcomes before determining the curriculum, activities and materials. This sequence enables students to have a deep understanding of the content taught.