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 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 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 3 and the common ratio is 2, what is the 4th term?

Back

The 4th term is a_4 = 3 * 2^(4-1) = 3 * 8 = 24.

Front

What is the common ratio of the sequence 5, 15, 45, ...?

Back

The common ratio is r = 15 / 5 = 3.

Front

Determine the next term in the geometric sequence 2, 6, 18, ...

Back

The next term is 54, found by multiplying the last term (18) by the common ratio (3).

Front

Write the equation for the nth term of the geometric sequence: 1, 3, 9, ...

Back

The equation is a_n = 1 * 3^(n-1).

Front

What is the common ratio of the sequence 100, 50, 25, ...?

Back

The common ratio is r = 50 / 100 = 0.5.

Front

Is the sequence 4, 8, 12, ... arithmetic, geometric, or neither?

Back

The sequence is arithmetic because the difference between consecutive terms is constant.

Front

If a geometric sequence has a common ratio of -2, what can you say about the terms?

Back

The terms will alternate in sign, as multiplying by a negative number changes the sign of the term.