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

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

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 common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

What is 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), where a_1 is the first term and r is the common ratio.

Front

What is the common ratio in the sequence 72, 36, 18, 9...?

Back

The common ratio is 1/2.

Front

What is the common ratio in the sequence -3, 6, -12, 24...?

Back

The common ratio is -2.

Front

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

Back

The next term is 32.

Front

What is the sum of the first 10 terms of the series 2 - 6 + 18 - 54 + ...?

Back

The sum is -29524.