Sequences, Series and Sigma Notation

Front

Define a sequence.

Back

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

Front

What is a series in mathematics?

Back

A series is the sum of the terms of a sequence.

Front

What is sigma notation?

Back

Sigma notation is a concise way to represent the sum of a sequence of numbers, using the Greek letter sigma (Σ) to denote summation.

Front

Write the sigma notation for the sum of the first n natural numbers.

Back

Front

What is the formula for the n-th term of an arithmetic sequence?

Back

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

Front

Find the first four terms of the sequence defined by a_n = 3n + 2.

Back

The first four terms are: 5, 8, 11, 14.

Front

What is the formula for the n-th term of a geometric sequence?

Back

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in the sequence is multiplied to get the next term.

Front

Write the series 1 + 2 + 3 + ... + n using sigma notation.

Back