Exploring Geometric Sequences

What is the common ratio of the sequence 2, 6, 18, 54?

• 6

• 4

• 2

• 3

Find the 5th term of the geometric sequence where the first term is 3 and the common ratio is 4.

• 256

• 1024

• 512

• 768

Calculate the sum of the first 6 terms of the geometric sequence 5, 15, 45, ...

• 1500

• 1820

• 600

• 3000

Convert the geometric sequence 1, 1/2, 1/4, ... into its general form.

• a_n = 2^(n-1)

• a_n = (1/2)^(n-1)

• a_n = (1/3)^(n-1)

• a_n = 1/(2n)

If the first term of a geometric sequence is 7 and the common ratio is 3, what is the 10th term?

• 729

• 2187

• 2401

• 137781

Determine the common ratio of the sequence 81, 27, 9, 3.

• 1/4

• 1/3

• 2/3

• 1/2

What is the sum of the first 4 terms of the geometric sequence with first term 2 and common ratio 5?

• 100

• 50

• 312

• 200

Express the geometric sequence 10, 20, 40, ... in terms of its nth term.

• 10 * 2^(n-1)

• 5 * 2^n

• 20 * 2^(n-2)

• 10 * 3^(n-1)

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

• 10

• 8

• 6

• 12

Find the sum of the first 5 terms of the geometric sequence where the first term is 1 and the common ratio is 1/3.

• 2.0

• 1.5

• 1.49382716049

• 0.5