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 for the sequence: 3, 15, 75, 375?

Back

5

Front

What is the common ratio for the sequence: 10, 20, 40, 80?

Back

2

Front

What is the next term in the sequence: 5, 25, 125, 625?

Back

3125

Front

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

Back

30

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 a geometric sequence and an arithmetic sequence?

Back

In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).

Front

What is the common ratio for the sequence: 2, 4, 8, 16?

Back

2

Front

If the first term of a geometric sequence is 3 and the common ratio is 4, what is the 5th term?

Back

The 5th term is 3 * 4^(5-1) = 3 * 256 = 768.