# Number Patterns

A number pattern is a unique quality that prevails in a set of numbers. More than 200 years back, an elementary school teacher in Germany wanted to engage the students of his class for some time by asking them to find the sum of all the numbers from 1 to 100. But one student amazed the teacher by telling the correct answer almost instantly. Because he found a pattern that every pair of numbers that are in the same place from either ends adds up to the same sum of 101. Hence the total is 50 pair’s times 101 = 5050. The student was none other than the great mathematician and scientist by his well-known name ‘Gauss’. Thus the existence of number pattern was noticed from ancient times.

A list of numbers which form a pattern is called a sequence. The
arithmetic and geometric sequences developed in Algebra are based on
number patterns. The set of numbers 1, 2, 3, 4 … exhibit a pattern that
the difference between any two successive terms is constant and that is
equal to 1. Such a sequence with a common difference (not necessarily 1
and could be any integer) is called an arithmetic sequence.

In a
geometric sequence, the pattern is the common ratio that exists between
consecutive terms. By applying the concept of number patterns, you can
predict any term in a sequence and also predict the sum of finite number
of terms. In fact, in a geometric sequence, if the common ratio is a
proper fraction, even the sum of infinite terms could be figured out.