A sequence of numbers begins:

What is the one-hundredth entry in this sequence?

Define

Which of the following expressions is equal to ?

The top row in the above diagram shows a sequence of figures. Which figure in the bottom row is the next one in the sequence?

Examine the above figure. In the top row, the cubes of the whole numbers are written in ascending order. In each successive row, each entry is the difference of the two entries above it - five of those entries have been calculated for you.

What is the fifth entry in the third row?

The above diagram shows a sequence of figures. In the fourth figure, each of the four variables, , , , and , is replaced by a value.

What value replaces ?

The above diagram shows a sequence of figures. In the fourth figure, each of the four variables, , , , and , is replaced by a value.

What value replaces ?

Define a sequence of numbers as follows:

For all integers ,

Evaluate .

Give the sum of the infinite geometric series that begins

Anya, Brian, Clark, and Donna represented Central High in a math contest. The team score is the sum of the three highest scores; Anya outscored Clark, Brian outscored Donna; Donna outscored Clark. Whose scores were added to determine the team score?

The above diagram shows a sequence of figures. In the fourth figure, each of the three variables, , , and , is replaced by a value.

What value replaces ?