Geometric Sequences and Recursive Formulas

This lesson covers geometric sequences, focusing on multiplication instead of addition or subtraction. It explains how to use multiplication to increase or decrease numbers in a sequence and introduces the concept of a common ratio. The lesson also covers writing recursive formulas for geometric sequences, emphasizing the importance of the first term and the common ratio. Strategies for finding the common ratio, even with large numbers, are discussed, and the process of writing a recursive formula is demonstrated.

What is the main operation used in a geometric sequence?

• Addition

• Subtraction

• Multiplication

• Division

In a geometric sequence, how do you make a number smaller?

• Multiply by a fraction

• Add a negative number

• Subtract a fraction

• Divide by a whole number

What two things are needed to write a recursive formula for a geometric sequence?

• Common ratio and last term

• Common difference and last term

• First term and common ratio

• First term and common difference

What is the term used instead of 'common difference' in a geometric sequence?

• Common sum

• Common product

• Common ratio

• Common factor

What is the first term in the sequence: 1, 5, 25, 125, 625?

• 1

• 125

• 5

• 25

If the first term is 1 and the common ratio is 5, what is the second term?

• 5

• 10

• 25

• 1

What is the common ratio in the sequence: 1, 5, 25, 125, 625?

• 3

• 4

• 5

• 6

How can you simplify finding the common ratio in a sequence with large numbers?

• Divide the numbers

• Guess the ratio

• Focus on smaller numbers

• Use a calculator

What letter is used to denote the sequence in the recursive formula example?

• b

• k

• a

• n

In the recursive formula, what operation is used with the common ratio?

• Subtraction

• Division

• Addition

• Multiplication