sequences and series cards

Series

Sum of a sequence

Sequence

A list of numbers in a specified order

Geometric

You would be multiplying by the common ratio, a.k.a. “R”

Arithmetic

Adding instead of multiplying by D, the common difference.

Arithmetic sequence formula

Arithmetic/series

Geometric sequence

Finite geometric series

Infinite geometric series

Sigma notation

A concise way to write a series

the image shows an example.

When dealing with problems involving percentage increases or decreases over time — like population growth, investment interest, or catches increasing daily — you’ll often see the common ratio r expressed as a decimal ___ than 1 for __ (like 1.15 for 15% increase).

• greater than

• Growth

For ______, you’d use a ratio ___ 1 (for example, 0.85 for a 15% decrease).

• decreases

• Less than