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 (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

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

Back

The nth term (a(n)) of a geometric sequence can be found using the formula: a(n) = a(1) * r^(n-1), where a(1) is the first term and r is the common ratio.

Front

What is the explicit formula for the geometric sequence 3, -12, 48, -192, ...?

Back

a(n) = 3(-4)^(n-1)

Front

Find the 11th term of the geometric sequence 64, -32, 16, -8, ...

Back

The 11th term is 0.0625.

Front

What is the common ratio of the sequence 4, -16, 64, -256, ...?

Back

The common ratio is r = -4.

Front

How do you determine the next three terms in the sequence -4, -12, -36, -108, ...?

Back

The next three terms are -324, -972, -2916.

Front

What is the formula to find the common ratio from two consecutive terms?

Back

The common ratio can be found using the formula r = a(n)/a(n-1), where a(n) is the current term and a(n-1) is the previous term.

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 5 * 3^(4-1) = 5 * 27 = 135.

Front

What is the relationship between the terms in a geometric sequence?

Back

Each term is obtained by multiplying the previous term by the common ratio.