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 can you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

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 5th term of the geometric sequence: 2, 6, 18, ...

Back

The 5th term is 162.

Front

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

Back

The 4th term is 192.

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) for r ≠ 1.

Front

Calculate the sum of the first 5 terms of the geometric sequence: 1, 2, 4, 8, ...

Back

The sum is 31.

Front

Is the sequence 5, 10, 20, 40, ... geometric?

Back

Yes, it is geometric with a common ratio of 2.

Front

What is the 10th term of the geometric sequence: 1, 3, 9, 27, ...?

Back

The 10th term is 19,683.