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 a geometric sequence.

Front

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

Back

6

Front

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

Back

-45

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Find the common ratio of the geometric sequence: 2, 6, 18, ...

Back

3

Front

What is the next term in the geometric sequence: 4, 12, 36, ...?

Back

108

Front

If the first term of a geometric sequence is 10 and the common ratio is 0.5, what is the fourth term?

Back

1.25

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum S_n of the first n terms can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where r is not equal to 1.

Front

If the common ratio of a geometric sequence is 1, what type of sequence is it?

Back

It is a constant sequence, where all terms are the same.