Geometric Sequence Review

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_n is the nth term, 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 of the sequence 2, 4, 8, 16?

Back

The common ratio is 2, since each term is multiplied by 2 to get the next term.

Front

Write the explicit formula for the geometric sequence with first term 7 and common ratio -1.

Back

a_n = 7 * (-1)^(n-1).

Front

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

Back

t(n) = 5 * (2^n).

Front

What is the next term in the sequence 2, 4, 8, 16?

Back

The next term is 32.

Front

If a geometric sequence has a first term of 3 and a common ratio of -4, what is the explicit formula?

Back

a_n = 3 * (-4)^(n-1).

Front

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

Back

The first term is 10.

Front

In the sequence defined by a_n = 4 * (3^(n-1)), what is the second term?

Back

The second term is 12.