Sequences and Series Review

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

Front

What is the formula for the nth term of a geometric sequence?

Back

Front

What is the sum of the first n terms of an arithmetic series?

Back

Front

What is the sum of the first n terms of a geometric series?

Back

Front

What is a convergent geometric series?

Back

A convergent geometric series is a geometric series where the absolute value of the common ratio is less than 1, leading to a finite sum.

Front

What is the formula for the sum of an infinite convergent geometric series?

Back

Front

How do you determine if a sequence is arithmetic or geometric?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. To determine if it is geometric, check if the ratio of consecutive terms is constant.