Exploring Arithmetic and Geometric Sequences

Mr. Bean introduces arithmetic and geometric sequences, explaining their definitions, properties, and how to calculate terms using formulas. He covers arithmetic sequences with a common difference and geometric sequences with a common ratio, providing examples and rules for each. The video concludes with a visual comparison of the two types of sequences.

What is a sequence?

• A mathematical operation

• A connected smooth curve

• A set of numbers listed in order

• A single number

What does the term 'arithmetic sequence' imply?

• The sequence is decreasing

• Each term has a common difference with the next

• Each term is divided by a common ratio

• Each term is multiplied by a common ratio

How do you calculate the nth term in an arithmetic sequence?

• Initial term - (n-1) * common difference

• Initial term / common difference

• Initial term * common ratio^n

• Initial term + (n-1) * common difference

In an arithmetic sequence, if the first term is 5 and the common difference is 3, what is the third term?

• 14

• 8

• 11

• 9

What is a geometric sequence?

• A sequence that decreases by the same amount

• A sequence that forms a straight line when graphed

• A sequence with a common ratio

• A sequence with a common difference

How do you find the common ratio in a geometric sequence?

• Subtracting successive terms

• Adding successive terms

• Multiplying successive terms

• Dividing a term by its preceding term

What does the term 'decreasing geometric sequence' imply?

• The common ratio is less than 1

• The common ratio is greater than 1

• The common difference is negative

• The sequence forms a straight line

How can you calculate any term in a geometric sequence?

• Initial term / common ratio^(n-1)

• Initial term + (n-1) * common ratio

• Initial term * common ratio^(n-1)

• Initial term - common ratio^n

What distinguishes an arithmetic sequence from a geometric sequence?

• Arithmetic sequences use division, while geometric sequences use subtraction

• There is no difference

• Geometric sequences use addition, while arithmetic sequences use multiplication

• Arithmetic sequences use addition, while geometric sequences use multiplication

In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the fourth term?

• 81

• 24

• 18

• 54