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 the sequence.

Front

How do you find 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

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?

Back

The 4th term is 3 * 2^(4-1) = 3 * 8 = 24.

Front

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

Back

The sum of the first n terms (S_n) of a geometric sequence is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

What is the common ratio for the sequence: 28, 14, 7, 3.5...?

Back

The common ratio is 1/2.

Front

What is the 14th term of the geometric sequence defined by a_n = 5 * 2^(n-1)?

Back

The 14th term is 5 * 2^(14-1) = 5 * 8192 = 40960.

Front

Find the next three terms of the sequence: -4, -12, -36, -108...

Back

The next three terms are -324, -972, -2916.

Front

What is a_5 in the sequence defined as a_n = 5 * 2^(n-1)?

Back

a_5 = 5 * 2^(5-1) = 5 * 16 = 80.

Front

Find the common ratio for the sequence: 4, -16, 64, -256...

Back

The common ratio is -4.