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 formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: 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

Find the first four terms of the sequence given the rule: a_n = 4(5)^(n-1)

Back

4, 20, 100, 500

Front

If Daisy received $2 on her first birthday and the amount tripled each year, how much will she receive on her 5th birthday?

Back

$162

Front

What is the common ratio in a geometric sequence?

Back

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

Front

What does 'r' represent in a geometric sequence?

Back

Common ratio.

Front

What is the 9th term in a geometric sequence with a common ratio of 2 and a first term of 3?

Back

768

Front

How do you find the common ratio of a geometric sequence?

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Front

What is the relationship between the first term and the common ratio in a geometric sequence?

Back

The first term is multiplied by the common ratio raised to the power of (n-1) to find the nth term.

Front

If the first term of a geometric sequence is 10 and the common ratio is 3, what are the first three terms?

Back

10, 30, 90.