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 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

Given the sequence 2, 6, 18, 54, what is the common ratio?

Back

The common ratio is 3, since each term is multiplied by 3 to get the next term.

Front

Write the explicit formula for the geometric sequence with first term 5 and common ratio 2.

Back

The explicit formula is a_n = 5 * 2^(n-1).

Front

Find the first four terms of the sequence defined by a_n = 3(4)^(n-1).

Back

The first four terms are 3, 12, 48, 192.

Front

Is the sequence 1, 2, 4, 8, ... geometric?

Back

Yes, it is geometric with a common ratio of 2.

Front

What is the common ratio for the sequence: 10, 30, 90...?

Back

The common ratio is 3.

Front

If a geometric sequence has a first term of 8 and a common ratio of 1/2, what is the 5th term?

Back

The 5th term is 8 * (1/2)^(5-1) = 8 * (1/16) = 0.5.

Front

Write the explicit formula for the sequence: 729, 243, 81...

Back

The explicit formula is a_n = 729 * (1/3)^(n-1).