Mathematics in Ancient and Medieval India c7.s2.9

c7.s2.9

*Arithmetic Progression*: Indian interest in the series began quite early in the Vedic age. A large number of Vedic series are mentioned in the *Taittirīya Saṃhitā*¹, *Vājasaneya Saṃhitā*² and *Pañcaviṃsa Brāhmaṇa*³. Some of the few such series are found in the *Bṛhaddevatā*⁴, *Śatapatha Brāhmaṇa*⁵, *Baudhāyana Śulba*⁶, Buddhist work *Dīgha Nikāya*⁷ and a Jain work *Antagoḍa Dasāo*⁸. The general rule for the summation of an A. P. : S = a + (a + b) + (a + 2b) + + [a + (n - 1)b] where S denotes the sum, a = first term, b = common difference and n = number of terms, is found in the *Bakhshālī Ms* ⁹ as follows: S = n [a + (n - 1) b/2 ]. Āryabhaṭa I¹⁰ (476 A. D. ) gave the above form as well as the form : S = n/2 (a + b). The same rule appears in the works of Brahmagupta¹ (628 A. D.), Mahāvīra² (850 A. D.), Śrīdhara³, Nemicandra⁴ and Bhāskara II⁵ (1150 A. D.). Āryabhaṭa I⁶ and all the above writers with the exception of Nemicandra gave also the sum of the following particular case :