Exploring Explicit and Recursive Formulas for Sequences

Mr. Allen explains how to identify arithmetic and geometric sequences, derive explicit and recursive formulas, and find the tenth term. He covers the common difference and ratio, and demonstrates calculations using both formulas. The video provides a comprehensive understanding of sequences, preparing students for various test scenarios.

What type of sequence is identified by alternating negative and positive terms?

• Arithmetic

• Geometric

• Fibonacci

• Linear

What is the common ratio of a geometric sequence that multiplies by -3?

• 1/3

• -1/3

• 3

• -3

How do you find the first term in an explicit formula for a geometric sequence?

• Multiply the common ratio by the first term

• Add the common ratio to the first term

• Raise the common ratio to the power of (n-1)

• Multiply the first term by the common ratio raised to the power of (n-1)

What indicates an arithmetic sequence?

• Multiplying by a constant

• Adding a constant

• Alternating signs

• Dividing by a constant

What is the common difference of an arithmetic sequence that decreases by 6 each term?

• -1/6

• 6

• 1/6

• -6

How is the explicit formula for an arithmetic sequence generally represented?

• a_n = a_1 - (n - 1)d

• a_n = a_1 / d^(n - 1)

• a_n = a_1 * r^(n - 1)

• a_n = a_1 + (n - 1)d

What is the purpose of simplifying the explicit formula of an arithmetic sequence?

• To find the common difference

• To determine the first term

• To make it easier to calculate terms

• To identify the sequence type

In a recursive formula, what does a_sub n depend on?

• The next term

• The previous term

• The common ratio

• The common difference

How do you find the tenth term of a sequence using an explicit formula?

• Substitute n with 10

• Add 10 to the first term

• Multiply the first term by 10

• Raise the common ratio to the power of 10

What was the tenth term of the arithmetic sequence discussed?

• 21

• -60

• 39

• -39