® The geometric mean (G.M.) of any two positive numbers a and b is given by ab i.e., the sequence a , G, b is G.P. Historical Note Evidence is found that Babylonians, some years ago, knew of arithmetic and geometric sequences. According to Boethius ( ), arithmetic and geometric sequences were known to early Greek writers. Among the Indian mathematician, Aryabhatta ( ) was the first to give the formula for the sum of squares and cubes of natural numbers in his famous work Aryabhatiyam, written around .
He also gave the formula for finding the sum to n terms of an arithmetic sequence starting with p th term. Noted Indian mathematicians Brahmgupta ( ), Mahavira ( ) and Bhaskara ( - ) also considered the sum of squares and cubes. Another specific type of sequence having important applications in mathematics, called Fibonacci sequence , was discovered by Italian mathematician Leonardo Fibonacci ( - ). Seventeenth century witnessed the classification of series into specific forms.
In James Gregory used the term infinite series in connection with infinite sequence. It was only through the rigorous development of algebraic and set theoretic tools that the concepts related to sequence and series could be formulated suitably.