Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 231

OHAPTER JI-ARITHMETICAL OPERATIONS.
largest common difference and any other remaining common difference is multiplied by the half of the number of terms lessened by one ; and when thie (product) is combined with one, (we get) O friend, the first terms of the various series having) the remaining (smaller) common differences,
Examples in illustration thereof. 90. Give out quickly, O friend, the first terms of all the serieu found in two sets of) such (series) as have equal sums (in relation to each set) and are characterised by 9 as the number of terms in each (series), when those (series belonging to the first and scuond sets) have respectively common differences beginning with I and ending with 6 (in one onso) and have 1, 3, 5 and 7 as the common differences in the other case).
The role for finding out the common difference in rolatiou to such (series in arithmetical progression) as are charactorised by varying first torms, equal numbers of terms and cqual sume :--
91. Of that (series) wbich has the largest first term, one is taken to be the common difference. The difforonce between this largest first term and (each of the) remaining (smaller) first toring is divided by the half of the number of terms lessened by ine; and when this (quotient in each (ANC) in combined with ono, (we get the conuinon differences of the various scries having) the remaining (smaller) first terms.
An (xample in illustration thereof. 9.2. O arithmetician, who bave seen the other shore of caloulation, give out the common differences of (all) those (series) which are characterized by equal gums and havd 1, 3, 5, 7, 9 and 11 for their first terms and 5 for the number of terms in each.
d and by their corresponding common differences. It is obvious that in this formula, when b, b, und, are given, a, in determined by chooning any valon for a; and one in chosen as the value of a in the rule here.
91. The general formula in this charis b = " + b, wherein alno the value of bis taken to be one in the rule
1-1
given above.