Understanding Arithmetic Sequences and Function Definitions

The video tutorial explains arithmetic sequences using a function f. It starts by introducing a sequence where each term is seven less than the previous one, and guides viewers to define the function explicitly. The tutorial then presents another example of an arithmetic sequence, where each term is 50 more than the previous one, and discusses different function definitions to verify their correctness. The video emphasizes understanding the arithmetic nature of sequences and how to express them through functions.

What is the common difference in the arithmetic sequence where the first term is 12 and the second term is 5?

• 5

• -5

• -7

• 7

If the first term of an arithmetic sequence is 12, what is the formula for the nth term?

• 12 + 7n

• 12 - 7n

• 12 + 7(n-1)

• 12 - 7(n-1)

How many times do you subtract 7 to find the third term of the sequence starting at 12?

• Once

• Twice

• Three times

• Four times

What is the first term of the new arithmetic sequence introduced in the video?

• -50

• 50

• 0

• -100

What is the common difference in the new arithmetic sequence starting at -100?

• -50

• -100

• 50

• 100

Which function definition correctly represents the sequence starting at -100 and increasing by 50?

• -150 + 50(n-1)

• -100 + 50n

• -150 + 50n

• -100 + 50(n-1)

What is the value of the second term in the sequence defined by -150 + 50n?

• -100

• 50

• -50

• 0

How can you verify that two different-looking function definitions are equivalent?

• By algebraic manipulation

• By checking the common difference

• By graphing the functions

• By checking the first term

What is the value of the third term in the sequence defined by -100 + 50(n-1)?

• 0

• -100

• 50

• -50

Which function definition does not correctly represent the sequence starting at -100?

• -150 + 50(n-1)

• -150 + 50n

• -100 + 50n

• -100 + 50(n-1)