Comparing Arithmetic and Geometric Sequences

Mr. Kilburn explains the differences between arithmetic and geometric sequences, focusing on recursive and explicit methods for each. He provides examples and clarifies common misunderstandings, emphasizing the importance of knowing the first term in recursive sequences. The tutorial covers how to calculate terms in both arithmetic and geometric sequences using formulas provided on reference sheets.

What type of sequence forms a straight line when graphed?

• Exponential sequence

• Arithmetic sequence

• Logarithmic sequence

• Geometric sequence

What is the common difference in the given arithmetic sequence: 3, -1, -5, ...?

• 3

• -3

• 4

• -4

In a recursive arithmetic sequence, what is essential to calculate the next term?

• The first term

• Both the first term and the common difference

• The last term only

• The common difference

What is necessary to start calculating terms in a recursive sequence?

• The common difference or ratio

• The last term of the sequence

• The first term of the sequence

• A formula from the reference sheet

What does an explicit formula allow you to do in an arithmetic sequence?

• Calculate any term directly

• Skip terms

• Find the common difference

• Only find the first term

How do you calculate the fifth term in an explicit arithmetic sequence?

• By adding the common difference to the first term 5 times

• By multiplying the common difference by 5

• By using the formula from the reference sheet

• By subtracting the common difference from the first term 5 times

What shape does a graph of a geometric sequence form?

• Exponential curve

• Parabola

• Circle

• Straight line

In a recursive geometric sequence, how do you find a term?

• By dividing the previous term

• By subtracting from the previous term

• By adding a constant

• By multiplying the previous term

What is the multiplier in the given geometric sequence: 6, 36, 216, ...?

• 6

• 30

• 216

• 6 squared

How do you find the fourth term in an explicit geometric sequence?

• By adding the common ratio to the first term 4 times

• By multiplying the first term by the common ratio 3 times

• By using the formula from the reference sheet

• By raising the first term to the power of 4