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

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 (r = a_n / a_(n-1)).

Front

Is the sequence 2, 4, 12, 48,... geometric?

Back

No, because the ratio between consecutive terms is not constant.

Front

What are the next 3 terms in the geometric sequence: 512, 256, 128, ___, ___, ___?

Back

64, 32, 16.

Front

Find the common ratio for the sequence: 64, -16, 4, -1,...

Back

r = -1/4.

Front

Find the common ratio for the sequence: 16, -4, 1, -1/4,...

Back

r = -1/4.

Front

Find the common ratio for the sequence: 10, 20, 40,...

Back

r = 2.

Front

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

Back

The nth term is given by 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 3 * 2^(5-1) = 48.

Front

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

Back

The sum S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.