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

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

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.

Front

What is a series?

Back

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

Front

Define common ratio in a geometric sequence.

Back

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

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.

Front

How do you find 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_n is the nth term.

Front

How do you find 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.

Front

What is the next term in the sequence: 2, 4, 8, 16, ...?

Back

The next term is 32, as this is a geometric sequence with a common ratio of 2.

Front

Identify the common difference in the sequence: 10, 7, 4, 1, ...

Back

The common difference is -3.