Problem Solving and Sequences
George Polya and How to Solve It
Arithmetic and Geometric Sequences
An arithmetic Sequence is a list of numbers in which consecutive numbers share a common difference.
Ex: 5, 10, 15, 20, 25,...
The common difference is 5.
Ex: 3, 6, 9, 12, 15,...
The common difference is 3.
A geometric sequence is a list of numbers in which consecutive numbers share a common ratio. Each number after the first is calculated by multiplying the preceding number by the common ratio.
Ex: 1, 4, 16, 64, 256,...
The common ratio is 4.
Ex: 2, 4, 8, 16, 32,...
The common ratio is 2.
Named after Fibonacci, also known as Leonardo of Pisa or Leonardo Pisano, Fibonacci numbers were first introduced in his Liber abaci in 1202. The son of a Pisan merchant, Fibonacci traveled widely and traded extensively. Math was incredibly important to those in the trading industry and his passion for numbers was cultivated in his youth.
Knowledge of numbers is said to have first originated in the Hindu-Arabic arithmetic system, which Fibonacci studied while growing up in North Africa. Prior to the publication of Liber abaci, the Latin-speaking world had yet to be introduced to the decimal number system. He wrote many books about geometry, commercial arithmetic and irrational numbers. He also helped develop the concept of zero.