Recursive and Arithmetic Sequences

This video tutorial introduces recursive formulas, explaining how they are used to find the nth term of a sequence by performing operations on the previous term. It covers the three main components of a recursive formula: the first term, the expression for the nth term, and the condition for n. The video provides examples of basic recursive formulas, differentiates between arithmetic and geometric sequences, and offers practice problems with solutions to reinforce understanding.

What does a recursive formula tell you?

• How to find the nth term by adding a constant value

• How to find the nth term by dividing by a constant value

• How to find the nth term by multiplying by a constant value

• How to find the nth term by performing operations on the previous term

In a recursive formula, what does 'a sub 1' represent?

• The common ratio of the sequence

• The previous term in the sequence

• The nth term of the sequence

• The first term in the sequence

If a sub 1 is 5 and the formula is a sub n = 2 * a sub n-1 + 1, what is the second term?

• 11

• 12

• 13

• 10

What is the third term in the sequence if a sub 1 is 6 and the formula is a sub n = 2 * a sub n-1?

• 48

• 24

• 18

• 12

How do you identify an arithmetic sequence?

• By checking if the terms are increasing or decreasing by a constant amount

• By checking if the terms are multiplying by a constant ratio

• By checking if the terms are dividing by a constant ratio

• By checking if the terms are adding a variable amount

What is the common ratio in the geometric sequence 0.5, 1, 2, 4?

• 0.5

• 1

• 2

• 4

What is the recursive formula for the arithmetic sequence -3, 2, 7, 12?

• a sub n = a sub n-1 + 5

• a sub n = a sub n-1 - 5

• a sub n = a sub n-1 * 5

• a sub n = a sub n-1 / 5

What is the first term (a sub 1) in the sequence 243, 81, 27, 9?

• 243

• 9

• 27

• 81

If a sub 1 is 3 and the formula is a sub n = 2 * a sub n-1 - 4, what is the fourth term?

• 8

• 4

• 0

• 2

What is the common ratio in the geometric sequence 8, -20, 50, -125?

• -2

• 2.5

• -2.5

• 3