Code Breaking

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.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last known term by the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

Given the sequence 4, 16, 64, what is the common ratio?

Back

The common ratio is 4, since 16/4 = 4 and 64/16 = 4.

Front

What is the next term in the sequence 5, 25, 125?

Back

The next term is 625, found by multiplying 125 by the common ratio of 5.

Front

How do you identify the next three terms in a geometric sequence?

Back

Multiply the last known term by the common ratio repeatedly to find the next three terms.

Front

What is the formula for 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 the next term in the sequence 4, 12, 36, 108?

Back

The next term is 324, found by multiplying 108 by the common ratio of 3.

Front

How do you find missing terms in a sequence?

Back

To find missing terms, identify the pattern (common difference or ratio) and apply it to fill in the gaps.

Front

What is the next term in the sequence 18, 24, ___, 36, 42?

Back

The missing term is 30, as the sequence increases by 6.