Sequences and Series

Front

What is a sequence?

Back

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

Front

What is a series?

Back

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

Front

Define common difference in an arithmetic sequence.

Back

The common difference is the constant amount that each term in an arithmetic sequence differs from the previous term.

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 after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

Define common ratio in a geometric sequence.

Back

The common ratio is the constant factor between consecutive terms in a geometric sequence.

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 an infinite geometric series?

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An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely.

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When does an infinite geometric series converge?

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An infinite geometric series converges if the absolute value of the common ratio is less than 1 (|r| < 1).

Front

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

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The sum S of an infinite geometric series can be calculated using the formula: S = a / (1 - r), where a is the first term and r is the common ratio.