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

What is the common ratio in the sequence 4, 16, 64?

Back

The common ratio is 4, as each term is multiplied by 4 to get the next term (4 x 4 = 16, 16 x 4 = 64).

Front

Find the next term in the geometric sequence: 4, 16, 64, ___.

Back

256.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

What is the common difference in the sequence 7, 14, 21, 28?

Back

The common difference is 7, as each term increases by 7 (14 - 7 = 7, 21 - 14 = 7, etc.).

Front

Find the next term in the arithmetic sequence: 7, 14, 21, 28, ___.

Back

35.

Front

How do you find the next three terms in the sequence 4, 12, 36, 108?

Back

Multiply the last term by 3 to find the next term: 108 x 3 = 324, then 324 x 3 = 972, and 972 x 3 = 2916.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

Find the next three terms in the geometric sequence: 5, 25, 125, 625, __, __, __.

Back

3125, 15625, 78125.