Sequences

Front

What is a sequence in mathematics?

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that is added to each term to get the next term in an arithmetic sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is a geometric sequence?

Back

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

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the constant factor by which each term is multiplied to obtain the next term in a geometric sequence.

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

Back

The sum can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Front

What is the formula for the sum of the first n terms of a geometric sequence?

Back

The sum can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1, where S_n is the sum of the first n terms.

Front

What is an alternating sequence?

Back

An alternating sequence is a sequence where the terms alternate in sign, such as -2, 2, -2, 2.

Front

What is the Fibonacci sequence?

Back

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.