Geometric Sequence

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 formula for the nth term of a geometric sequence?

Back

The nth term (a_n) 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 does 'r' represent in a geometric sequence?

Back

In a geometric sequence, 'r' represents the common ratio, which is the factor by which we multiply each term to get the next term.

Front

What does 'a_1' represent in a geometric sequence?

Back

In a geometric sequence, 'a_1' represents the first term of the sequence.

Front

What is the 5th term of the sequence 7, 14, 28, ...?

Back

112

Front

If a_1 = 1 and r = 2, what is the value of the 4th term?

Back

8

Front

Which of the following is a geometric sequence? 2, 4, 5, ...; 2, 6, 18, ...; 2, 4, 6, ...; 10, 20, 200, ...?

Back

2, 6, 18, ...

Front

What is the common ratio of the sequence 3, 6, 12, 24, ...?

Back

The common ratio is 2.

Front

How do you find the common ratio in a geometric sequence?

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Front

What is the 3rd term of the geometric sequence where a_1 = 5 and r = 3?

Back

45