ALG Unit 3: 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 in the sequence by the previous term (r = a_n / a_(n-1)).

Front

What are the next three terms in the geometric sequence: 512, 256, 128?

Back

The next three terms are 64, 32, and 16.

Front

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

Back

The nth term of a geometric sequence can be expressed as 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 10 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 10 * 2^(5-1) = 10 * 16 = 160.

Front

What is the common ratio of the sequence defined by a_n = 10(2)^(n-1)?

Back

The common ratio (r) of the sequence is 2.

Front

How can you determine if a sequence is geometric?

Back

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

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio.

Front

Given the sequence 3, 6, 12, 24, what is the common ratio?

Back

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

Front

What is the 3rd term in the geometric sequence where a_1 = 5 and r = 3?

Back

The 3rd term is 5 * 3^(3-1) = 5 * 9 = 45.