Geometric Sequence

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 formula for the nth term of a geometric sequence?

Back

The nth term 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 does a_1 represent in a geometric sequence?

Back

a_1 represents the first term of the geometric sequence.

Front

How do you find the common ratio (r) in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term in the sequence.

Front

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

Back

The second term is 5 * 3 = 15.

Front

What is the common ratio of the geometric sequence 2, 6, 18, 54, ...?

Back

The common ratio is 3, since each term is multiplied by 3 to get the next term.

Front

Write the explicit formula for the geometric sequence 4, 12, 36, 108, ...

Back

The explicit formula is a_n = 4 * 3^(n-1).

Front

What is the 5th term in a geometric sequence with a first term of 2 and a common ratio of 4?

Back

The 5th term is 2 * 4^(5-1) = 2 * 256 = 512.

Front

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

Back

If the common ratio is 1, the sequence is a constant sequence, where all terms are the same.

Front

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

Back

The sum 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.