Geometric Sequence

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 in a geometric sequence?

Back

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

Front

How do you find the common ratio of 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

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the first term of the geometric sequence 3, -12, 48, -192, ...?

Back

The first term (a_1) is 3.

Front

What is the common ratio of the sequence 3, -12, 48, -192, ...?

Back

The common ratio (r) is -4.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Front

What is the 9th term of a geometric sequence with a first term of 3 and a common ratio of 2?

Back

The 9th term is 768.

Front

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

Back

The 4th term is 135.

Front

What is the formula to find the nth term of a geometric sequence?

Back

The nth term can be found using the formula a_n = a_1 * r^(n-1).