Fibonacci Sequence and Tiling Identities Quiz

What is the starting point of the Fibonacci sequence?

• 0 and 1

• 2 and 3

• 3 and 5

• 1 and 1

How is the next term in the Fibonacci sequence traditionally calculated?

• By subtracting the previous term from the next

• By dividing the previous term by the next

• By adding the previous two terms

• By multiplying the previous two terms

What is the new identity introduced for calculating even-indexed Fibonacci terms?

• f_sub_2n = fn^2 + fn-1^2

• f_sub_2n = fn^2 - fn-1^2

• f_sub_2n = fn + fn-1

• f_sub_2n = fn * fn-1

In the tiling analogy, what do the one square pieces and two square domino pieces represent?

• The Fibonacci numbers

• The terms of the sequence

• The recurrence relation

• The ways to tile a row of squares

What is the significance of the middle two squares in the tiling analogy for even-indexed terms?

• They are always covered by a single piece

• They are not considered in the tiling

• They determine the number of ways to tile the row

• They are always left uncovered

How can F100 be calculated using the new identity?

• By finding F50 and F49

• By finding F75 and F74

• By finding F99 and F98

• By finding F25 and F24

What is the structure of a row of 2n + 1 squares in the odd-indexed identity?

• n squares plus another one plus n more

• 2n squares plus one

• n squares plus two

• 2n squares

In the odd-indexed identity, what happens if the middle square is covered by a single square piece?

• The row is covered by a domino

• The row is left uncovered

• The row is ignored

• The row is divided into two separate rows

What is the result of doubling f_sub_2 * f_sub_1 in the odd-indexed identity?

• It gives the sum of the terms

• It gives the square of the term

• It gives the next Fibonacci term

• It gives the product of the terms

What is the main benefit of using these new identities for Fibonacci terms?

• They are not useful

• They simplify calculations

• They complicate the process

• They are only theoretical