Understanding Sequences and Formulas

The video tutorial explains how to determine formulas for different types of sequences by analyzing patterns. It covers arithmetic sequences, sequences of fractions, and alternating sequences. The tutorial provides step-by-step methods to derive formulas and verify their correctness, including handling alternating signs and powers in sequences.

What is the first step in determining the formula for a sequence?

• Using a calculator

• Checking the formula with random numbers

• Analyzing the sequence for patterns

• Guessing the formula

In the sequence 1, -3, -7, -11, what is the common difference?

• -4

• -3

• -5

• -6

How can repeated addition be expressed in a formula?

• Using subtraction

• Using exponents

• Using division

• Using multiplication

Which of the following is a correct way to express the formula for a sequence?

• A sub n = 5 + 4n

• A sub n = 1 + 4n

• A sub n = 5 - 4n

• A sub n = 1 - 4n

What is the formula for a sequence where all numerators are 2 and denominators are powers of 3?

• A sub n = 3^n / 2

• A sub n = 2^n / 3

• A sub n = 3 / 2^n

• A sub n = 2 / 3^n

What is a key characteristic of an alternating sequence?

• Terms are all fractions

• All terms are positive

• Terms alternate between positive and negative

• All terms are negative

How do you modify a formula to account for alternating signs in a sequence?

• Subtract a constant

• Divide by two

• Multiply by negative one raised to a power

• Add a constant

In the sequence 6, 11, 16, 21, what is the common difference?

• 6

• 7

• 4

• 5

What is the formula for the non-alternating sequence 6, 11, 16, 21?

• A sub n = 6 + 5n

• A sub n = 1 + 5n

• A sub n = 6 + 5(n-1)

• A sub n = 1 + 5(n-1)

What is the result of multiplying a sequence formula by negative one to a power?

• It doubles the sequence values

• It makes the sequence alternate in sign

• It changes the sequence to all negative terms

• It changes the sequence to all positive terms