What is a common ratio?

A common ratio is a consistent factor by which each term in a sequence is multiplied to get the next term. In geometric sequences, the common ratio is calculated by dividing any term in the sequence by the preceding term.

For example, in the sequence 2, 4, 8, 16, 32, the common ratio is 2, as each term is twice the preceding term.

Common ratios are important in mathematics, particularly in the study of sequences and series. They can be used to predict future terms in a sequence, calculate the sum of an infinite series, or determine if a series converges or diverges.