The ancient Greeks studied figurate numbers, so named because of their representations as...

The ancient Greeks studied figurate numbers, so named because of their representations as geometric arrangements of points.

Triangular Numbers

Square Numbers

Pentagonal Numbers

a. Use inductive reasoning to write the five triangular numbers that follow 21.

b. Use inductive reasoning to write the five square numbers that follow 25.

c. Use inductive reasoning to write the five pentagonal numbers that follow 22.

d. Use inductive reasoning to complete this statement: If a triangular number is multiplied by 8 and then 1 is added to the product, a ______ number is obtained.