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

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 formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence 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

What is the recursive rule for a geometric sequence?

Back

The recursive rule for a geometric sequence is: a_n = r * a_(n-1), where r is the common ratio.

Front

Is the sequence 2, 4, 12, 48 a geometric sequence?

Back

No, this sequence is not geometric because the ratio between consecutive terms is not constant.

Front

Find the common ratio for the sequence: 28, 14, 7, 3.5...

Back

The common ratio is 1/2.

Front

What is the 11th term of the sequence: 64, -32, 16, -8...?

Back

The 11th term is 0.0625.

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 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

What happens to the terms of a geometric sequence if the common ratio is less than 1?

Back

If the common ratio is less than 1, the terms of the sequence will decrease and approach zero.