Front

What is a sequence in mathematics?

Back

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

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CCSS.HSF.BF.A.2

Front

Define an arithmetic sequence.

Back

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

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

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.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

Front

What is a series in mathematics?

Back

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

Tags

CCSS.HSA.SSE.B.4

Front

Define the summation notation.

Back

Summation notation is a way to represent the sum of a sequence of numbers using the Greek letter sigma (Σ).

Front

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

Back

The sum (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where 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 series?

Back

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

Tags

CCSS.HSA.SSE.B.4

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms.

Tags

CCSS.HSF.BF.A.2