Geometric Sequences - Recursive Formula | Algeb...

What is a sequence in mathematics?

• A list of numbers that follow a pattern.

• A random collection of numbers.

• A single number.

• A picture made of shapes.

How can you tell if a sequence is a geometric sequence?

• By adding the same number to get the next term.

• By multiplying or dividing by the same number to get the next term.

• By looking at the first number.

• By subtracting the same number to get the next term.

What is the common ratio (r) for the geometric sequence: 2, 6, 18, 54, ...?

• 2

• 3

• 4

• 6

In the geometric sequence 5, 10, 20, 40, ..., what is the first term (a_1)?

• 10

• 20

• 40

• 5

Which of the following is the recursive formula for a geometric sequence?

• a_n = a_{n-1} + r

• a_n = a_{n-1} * r

• a_n = n * r

• a_n = a_1 + (n-1)d

A geometric sequence has a first term (a_1) of 10 and a common ratio (r) of -2. What is the recursive formula for this sequence?

• a_1 = 10; a_n = a_{n-1} + (-2)

• a_1 = 10; a_n = a_{n-1} * (-2)

• a_1 = -2; a_n = a_{n-1} * 10

• a_n = 10 * (-2)

If the first term (a_1) of a geometric sequence is 3 and the common ratio (r) is 4, what is the second term (a_2)?

• 7

• 12

• 16

• 3

For a geometric sequence where a_1 = 5 and the common ratio r = 3, what is the third term (a_3)?

• 15

• 45

• 25

• 75

Given the recursive formula: a_1 = 8, a_n = a_{n-1} * (1/2). What is the first term of this sequence?

• 1/2

• 4

• 8

• 16

Using the recursive formula: a_1 = 16, a_n = a_{n-1} * (-1/4). What is the second term (a_2)?

• -4

• 4

• 16

• -1/4