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 the sequence.

Front

Find the common ratio for the sequence: 2, 6, 18, 54...

Back

r = 3

Front

Find the common ratio for the sequence: 5, 20, 80, 320...

Back

r = 4

Front

Find the common ratio for the sequence: 1, 1/2, 1/4, 1/8...

Back

r = 1/2

Front

What does the term 'n' represent in the formula for the nth term of a geometric sequence?

Back

In the formula a_n = a_1 * r^(n-1), 'n' represents the term number in the sequence.

Front

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

Back

The nth term is given by 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 sum of the first n terms of a geometric sequence?

Back

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

Front

Find the common ratio for the sequence: 10, 5, 2.5, 1.25...

Back

r = 1/2