11/19 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

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

What is the formula for the nth term of a geometric sequence?

Back

The nth term 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

What is the recursive formula for a geometric sequence?

Back

The recursive formula for a geometric sequence is: a_n = r * a_(n-1), where r is the common ratio.

Front

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the 5th term?

Back

The 5th term a_5 = 5 * 2^(5-1) = 5 * 16 = 80.

Front

What is the common ratio of the sequence 64, -16, 4, -1?

Back

The common ratio r = -1/4.

Front

What is the common ratio of the sequence 2, -12, 72?

Back

The common ratio r = -6.

Front

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

Back

To find the next term in a geometric sequence, multiply the last known term by the common ratio.

Front

What is the first term of the geometric sequence defined by a_n = 3 * 5^(n-1)?

Back

The first term a_1 = 3 * 5^(1-1) = 3 * 1 = 3.

Front

If a geometric sequence has a common ratio of 1/2 and the first term is 8, what is the 4th term?

Back

The 4th term a_4 = 8 * (1/2)^(4-1) = 8 * (1/2)^3 = 8 * 1/8 = 1.