MA19.PRE.15

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.15
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems, extending to infinite geometric series.

Unpacked Content

Knowledge

Students know:

Characteristics of a geometric series.
Techniques for performing algebraic manipulations and justifications for the equivalence of the resulting expressions.

Skills

Students are able to:

Identify the regularity that exists in a series as being that which defines it as a geometric series.
Accurately perform the procedures involved in using geometric series to solve contextual problems,
Explain with mathematical reasoning why each step in the derivation of the formula for the sum of a finite geometric series is legitimate, including explaining why the formula does not hold for a common ratio of 1.

Understanding

Students understand that:

When each term of a geometric series is multiplied by a value, the result is a new geometric series.
When many problems exist with the same mathematical structure, formulas are useful generalizations for efficient solution of problems, (e.g., mortgage payment calculation with geometric series).

Vocabulary

Geometric series (finite and infinite)
Common ratio

COS Examples

Examples: calculate mortgage payments; determine the long-term level of medication if a patient takes 50 mg of a medication every 4 hours, while 70% of the medication is filtered out of the patient’s blood.