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

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 is the recursive formula for a geometric sequence?

Back

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

Front

Find the next three terms of the geometric sequence: 3, 6, 12, __, __, __.

Back

The next three terms are 24, 48, 96.

Front

Is the sequence 1, 3, 9, 27, ... geometric?

Back

Yes, this sequence is geometric because each term is multiplied by 3 to get the next term.

Front

Determine if the sequence 5, 10, 20, 40, ... is geometric.

Back

Yes, this sequence is geometric with a common ratio of 2.

Front

What does 'a_1' represent in a geometric sequence?

Back

a_1 represents the first term of the geometric sequence.

Front

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

Back

The 4th term is 54.

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) for r ≠ 1.