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 common ratio in a geometric sequence?

Back

To find the common ratio, divide any term in the sequence by the previous term.

Front

What is the common ratio of the sequence 3, 15, 75, 375?

Back

5

Front

What is the next term in the sequence 7, 14, 21, 28?

Back

35

Front

What are the next three terms in the sequence 5, 25, 125, 625?

Back

3125, 15625, 78125

Front

What is the rule for the sequence 97, 86, 75, 64?

Back

-11

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 difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence adds a constant value (common difference) to each term, while a geometric sequence multiplies by a constant value (common ratio).

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

Front

What is the common ratio of the sequence 10, 5, 2.5, 1.25?

Back

1/2