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 in a geometric sequence?

Back

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

Front

How do you find the next term in a geometric sequence?

Back

To find the next term, multiply the last known term by the common ratio.

Front

What is the explicit formula for a geometric sequence?

Back

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

Front

Given the sequence 4, 16, 64, what is the next term?

Back

The next term is 256.

Front

Find the common ratio for the sequence 4, -16, 64, -256, ...

Back

The common ratio is -4.

Front

Write the explicit formula for the geometric sequence 7, -7, 7, -7, ...

Back

The explicit formula is a_n = 7(-1)^(n-1).

Front

Write the explicit formula for the geometric sequence 100, 50, 25, ...

Back

The explicit formula is a_n = 100(1/2)^(n-1).

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 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).