Geometric Explicit Recursive

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 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

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

Back

The common ratio is 1/2.

Front

Identify the type of sequence: 300, 150, 75, 37.5...

Back

This is a geometric sequence.

Front

Write the explicit rule for the general term of the sequence 5, 15, 45...

Back

The explicit rule is a_n = 5(3)^(n-1).

Front

What is the first term of the geometric sequence defined by a_n = 10(2)^(n-1)?

Back

The first term (a_1) is 10.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

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).

Front

What is the common ratio for the geometric sequence defined by a_n = 5(3)^(n-1)?

Back

The common ratio is 3.