Understanding Arithmetic Sequences: Explicit and Recursive Formulas

This video tutorial explains the difference between explicit and recursive formulas for arithmetic sequences. It provides examples to illustrate how each formula is used to find terms in a sequence. The explicit formula is used to find the nth term directly, while the recursive formula uses the previous term to find the next one. The video includes step-by-step examples and concludes with a summary of the key differences between the two formulas.

What is the main difference between an explicit formula and a recursive formula in arithmetic sequences?

• Both formulas use the first term.

• Explicit formula uses the first term, recursive uses the previous term.

• Both formulas use the previous term.

• Recursive formula uses the first term, explicit uses the previous term.

In the explicit formula for arithmetic sequences, what does 'n' represent?

• The nth term

• The first term

• The previous term

• The common difference

How do you calculate the common difference in an arithmetic sequence?

• Subtract the first term from the last term

• Subtract any term from the previous term

• Add the first term to the last term

• Multiply the first term by the common ratio

What is the explicit formula for the sequence with a first term of 5 and a common difference of 4?

• a_n = 5n - 4

• a_n = 5 * n + 4

• a_n = 5 + (n - 1) * 4

• a_n = 4n + 5

In a recursive formula, what does 'a_(n-1)' represent?

• The common difference

• The previous term

• The nth term

• The first term

How is the nth term calculated in a recursive formula?

• By adding the common difference to the first term

• By subtracting the common difference from the previous term

• By adding the common difference to the previous term

• By multiplying the common difference by the nth term

What is the explicit formula for the sequence with a first term of 5 and a common difference of 3?

• a_n = 3n + 5

• a_n = 5n - 3

• a_n = 3n - 1

• a_n = 5 + (n - 1) * 3

In the second example, what is the common difference used in the explicit formula?

• 2

• 3

• 5

• 4

How do you find the third term using the recursive formula with a common difference of 3?

• Subtract 3 from the second term

• Multiply the second term by 3

• Add 3 to the second term

• Add 3 to the first term

What is the value of the third term in the sequence with a first term of 5 and a common difference of 3 using the recursive formula?

• 10

• 9

• 8

• 11