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

The common ratio (r) can be found by dividing any term by the previous term in the sequence.

Front

What is the next term in the geometric sequence 4, 16, 64, ...?

Back

256

Front

What is the common ratio of the sequence 4, -16, 64, -256, ...?

Back

r = -4

Front

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

Back

3125, 15625, 78125

Front

Fill in the missing number in the sequence 18, 27, __, 45, 54.

Back

36

Front

What number belongs in the blank 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 (a_n) can be calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 48.

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum S_n of the first n terms can be calculated using the formula S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.