Writing Arithmetic Sequences Recursively and Explicitly

The video tutorial explains arithmetic sequences, focusing on explicit and recursive rules. It begins with an introduction to arithmetic sequences and the explicit rule, followed by deriving the explicit rule for a given sequence and finding specific terms. The tutorial addresses common misunderstandings, emphasizing the importance of a consistent difference in arithmetic sequences. It then explores recursive sequences, providing examples and comparing them with explicit rules. The lesson concludes by summarizing the key points about arithmetic sequences and their representation.

What is the explicit formula for an arithmetic sequence with a common difference of 3 and a first term of 1?

• a_n = 3n + 1

• a_n = 3n - 2

• a_n = 3n - 1

• a_n = 3n + 2

Which of the following sequences is NOT arithmetic?

• 7, 14, 21, 28

• 3, 5, 8, 12

• 2, 4, 6, 8

• 5, 10, 15, 20

In a recursive sequence, how is each term determined?

• By subtracting a constant from the previous term

• By adding a constant to the previous term

• By multiplying the previous term by a constant

• By adding a constant to the first term

What is the explicit rule for an arithmetic sequence with a common difference of 4 and a first term of 1?

• a_n = 4n - 3

• a_n = 4n + 1

• a_n = 4n - 1

• a_n = 4n + 3

Using the explicit rule a_n = 4n - 3, what is the sixth term of the sequence?

• 21

• 25

• 23

• 19

What is the recursive rule for an arithmetic sequence with a common difference of 4?

• a_n = a_(n-1) + 4

• a_n = a_(n-1) + 5

• a_n = a_(n-1) + 3

• a_n = a_(n-1) + 2

If the fifth term of a sequence is 17 and the common difference is 4, what is the sixth term?

• 20

• 19

• 21

• 22