Understanding Sequences and Formulas

The video tutorial explains how to determine the formula for a sequence of fractions with alternating signs. It involves analyzing the numerator and denominator separately, identifying patterns, and deriving formulas. The numerator follows an arithmetic pattern, while the denominator follows a geometric pattern. The tutorial combines these formulas and adjusts for alternating signs using powers of negative one. The final formula is verified with specific terms to ensure accuracy.

What is the first step in analyzing a sequence of fractions?

• Combine the numerator and denominator

• Analyze the numerator and denominator separately

• Ignore the alternating signs

• Use only the denominator sequence

What pattern is observed in the numerator sequence?

• Division

• Multiplication

• Subtraction

• Addition

How is repeated addition expressed in the formula for the numerator?

• Using multiplication

• Using division

• Using subtraction

• Using exponents

What is the pattern observed in the denominator sequence?

• Division

• Subtraction

• Addition

• Multiplication

How is repeated multiplication expressed in the formula for the denominator?

• Using division

• Using addition

• Using subtraction

• Using exponents

What is the simplified formula for the numerator?

• 5 + 2n

• 9 + 2n

• 7 + 2n

• 11 + 2n

What is the formula for the denominator?

• 4^n

• 2^n

• n^4

• n^2

How do you adjust the formula to account for alternating signs?

• Add a factor of 2

• Subtract a factor of 1

• Add a factor of negative one to the power of n

• Multiply by zero

What is the result of negative one to the power of one?

• Two

• Negative one

• Zero

• Positive one

What is the correct formula for the original sequence?

• a_n = (11 + 2n) / 4^n

• a_n = (5 + 2n) / 4^n

• a_n = (9 + 2n) / 4^n

• a_n = (7 + 2n) / 4^n