Geometric Sequences

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 (r) in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what are the first five terms?

Back

3, 6, 12, 24, 48

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: g_n = g_1 * r^(n-1), where g_1 is the first term and r is the common ratio.

Front

What does g_1 represent in a geometric sequence?

Back

g_1 represents the first term of the geometric sequence.

Front

Is the sequence 2, 6, 18, 54 a geometric sequence?

Back

Yes, because each term is multiplied by 3 to get the next term.

Front

What are the next three terms in the geometric sequence: 81, 27, 9, ___, ___, ___?

Back

3, 1, 1/3

Front

If a geometric sequence has a common ratio of -2, what is the second term if the first term is 5?

Back

The second term is -10 (5 * -2).

Front

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

Back

The sum S_n = g_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

What does the term 'geometric mean' refer to?

Back

The geometric mean is the middle term in a geometric sequence of three numbers.