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 common ratio in a geometric sequence?

Back

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

Front

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

Back

The second term is 2 * 3 = 6.

Front

What does a₁ represent in a geometric sequence?

Back

a₁ represents the first term of the geometric sequence.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula a_n = a₁ * r^n-1, where a₁ is the first term and r is the common ratio.

Front

What is the explicit formula for the geometric sequence 5, 15, 45, ...?

Back

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

Front

Find the 4th term of the geometric sequence 1, 2, 4, ...

Back

The 4th term is 8.

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 common ratio of 1/2 and the first term is 8, what is the 5th term?

Back

The 5th term is 8 * (1/2)⁴ = 0.5.

Front

What are the next three terms in the sequence 2, 6, 18, ...?

Back

The next three terms are 54, 162, 486.