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

The common ratio (r) can be found by dividing any term 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

Given the sequence 10, 20, 40, 80, what is the common ratio?

Back

The common ratio is 2, since each term is multiplied by 2 to get the next term.

Front

Write the explicit formula for the geometric sequence 5, 15, 45, ...

Back

a_n = 5(3)^(n-1).

Front

What is the 11th term of the sequence 64, -32, 16, -8, ...?

Back

The 11th term is 0.0625.

Front

Identify the common ratio for the sequence 7, -7, 7, -7, ...

Back

The common ratio is -1.

Front

What sequence is represented by the equation 2(7)^(n-1)?

Back

The sequence is 2, 14, 98, 686... (where each term is multiplied by 7).

Front

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

Back

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

Front

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

Back

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