Geometric Sequences - Explicit Formula

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 in the sequence by the previous term: r = a_n / a_(n-1).

Front

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

Back

The second term is 3 * 2 = 6.

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 5th term of a geometric sequence with a first term of 4 and a common ratio of 3?

Back

The 5th term is 4 * 3^(5-1) = 4 * 81 = 324.

Front

What is the common ratio if the first three terms of a geometric sequence are 2, 6, and 18?

Back

The common ratio is 6 / 2 = 3.

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms as n increases?

Back

The terms will decrease and approach zero as n increases.

Front

What is the 14th term of a geometric sequence with a first term of 1 and a common ratio of 2?

Back

The 14th term is 1 * 2^(14-1) = 8192.

Front

How do you determine if a sequence is geometric?

Back

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

Front

What is the common ratio for the geometric sequence 5, 15, 45?

Back

The common ratio is 15 / 5 = 3.