Lecture Notes: Sequences, Series, and Financial Applications (Competencies)

Vocabulary flashcards covering sequences, series, arithmetic and geometric sequences, sigma notation, and related financial applications.

What is an example of an arithmetic sequence in real life?

Savings plans where a fixed amount is added regularly.

What is an example of a geometric sequence in real life?

Compound interest, where growth is proportional to the current amount.

How is the common ratio (r) calculated in a geometric sequence?

By dividing any term by its preceding term ($r = a<em>n / a</em>{n-1}$).

How is the common difference (d) calculated in an arithmetic sequence?

By subtracting any term from its preceding term ($d = a<em>n - a</em>{n-1}$).

Identify and describe patterns

Represents the position of the