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 formula for the nth term of a geometric sequence?

Back

The nth term (a_n) of a geometric sequence can be calculated using the formula: 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) = 3 * 16 = 48.

Front

What is the common ratio for the sequence: 28, 14, 7, 3.5...?

Back

The common ratio is 1/2.

Front

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

Back

The common ratio is r = -4.

Front

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

Back

The sequence is 2, 14, 98, 686... (where n = 1, 2, 3, ...).

Front

Find the 11th term for the sequence: 64, -32, 16, -8,...

Back

The 11th term is 0.0625.

Front

What is the common ratio for the sequence: 7, -7, 7, -7,...

Back

The common ratio is -1.

Front

What happens to the terms of a geometric sequence if the common ratio is less than 1?

Back

If the common ratio is less than 1, the terms of the sequence will decrease and approach zero.