Understanding Geometric Sequences

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a constant ratio.

Front

Identify the common ratio in the sequence: 2, 6, 18, 54.

Back

3

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the second term?

Back

15

Front

General formula for the nth term of a geometric sequence.

Back

a_n = a_1 * r^(n-1)

Front

Calculate the 5th term of the geometric sequence: 4, 12, 36, ...

Back

324

Front

If the 3rd term of a geometric sequence is 24 and the common ratio is 2, what is the first term?

Back

6

Front

Sum of the first 4 terms of the geometric sequence: 1, 3, 9, ...

Back

40

Front

How do you find the common ratio if you know two consecutive terms of a geometric sequence?

Back

r = b / a

Front

If a geometric sequence has a first term of 10 and a common ratio of 0.5, what is the 6th term?

Back

0.3125

Front

Explain how geometric sequences differ from arithmetic sequences.

Back

Geometric sequences have a constant ratio; arithmetic sequences have a constant difference.