Exploring Arithmetic and Geometric Sequences

This video lesson by Mrs. Chench introduces arithmetic and geometric sequences, explaining their definitions, examples, and differences. It covers finite and infinite sequences, sequence notation, and generalization. The lesson delves into arithmetic sequences, highlighting the common difference and its relation to linear functions, and geometric sequences, focusing on the common ratio and exponential functions. The video concludes with a comparison of the two sequence types and practice exercises.

What is the rule for Luis's sequence?

• Add 30 each month

• Divide by 30 each month

• Subtract 30 each month

• Multiply by 30 each month

What makes a sequence finite?

• It is defined by a subtraction rule

• It only contains positive numbers

• It has a fixed number of terms

• It continues indefinitely without any end

What is the common difference in Mrs. Gench's sequence?

• -40

• 40

• -30

• 30

How do you find the future term in an arithmetic sequence using an explicit formula?

• By multiplying the common difference with the term number

• By adding the common difference times (n-1) to the first term

• By dividing the first term by the common difference

• By adding the common difference to the first term

What is required to set up a recursive formula for an arithmetic sequence?

• Only the first term

• The first term and the common difference

• The last term and the common difference

• The previous term and the common difference

What is the common difference in the arithmetic sequence discussed?

• 4

• 6

• -4

• 12

What is the common ratio in the first geometric sequence example?

• 4

• 0.5

• 2

• -2

How is the future term in a geometric sequence calculated using an explicit formula?

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

• First term / common ratio^(n-1)

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

• First term * common ratio^(n-1)

What is the ninth term in the geometric sequence that alternates signs?

• -1/256

• 1/512

• -1/512

• 1/256

Which sequence is neither arithmetic nor geometric?

• 2, 6, 18, 54

• 3, 6, 9, 12

• 1/3, 2/5, 3/7, 4/9

• 2, 4, 8, 16