पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२२०

22 this (antyudhana) and the first term (gives) the madhyadhana. The product of this (madhyadhana) and the number of terms (in the series gives) the desired sum of all the terms therein. GANITASARASANGRAHA. Examples in illustration ther cof 65. (Each of) ten inerchants gives away money (in an anith- metically progressive series) as a religions offering, the first terms of the (ten) series being from 1 to 10, the common difference (in cach of these series) being of the same value (as the first terms thereof), and the number of terms being 10 (in every one of the series). Calculate the sums of those (series). 66. A certain excellent sravaka gave gems in offering to 5 temples (one after another) commencing the offering) with 2 (gems), and then increasing (it successively) by 3 (gems). O you who know how to calculate, mention what their (total) number is. 67. The first ternu is 3; the common difference is 8; and the number of terus is 12. All these three (quantities) are (gradu- ally) increased by 1, uutil (there are) 7 (series) O arithmetician, give out the sums of all (those series). 68. O you who possess enough strength of arms to cross the ocean of arithmetic, give out the total value of the offerings made in relation to 1000 cities, commencing (the offering) with 4 and increasing it successively by 8. The rule for finding out the number of terms (in a series in arithmetical progression) :- 69. When, to the square root of the quantity obtained by the addition of the square of the difference between twice the first It is quite obvious that an arithmetically progressive scries having a negative common difference becomes changed into one with a positive common differenco when the order of the terms is reversed throughout so as to make the last of them become the first 66. A śravaka is a lay follower of the Jaina religion, who merely hears, 2.e., listens to and learns the dharmas or duties, as opposed to the ascetics who are entitled to teach those religious duties. 69. Algebraically this rule works out thus -- √(2ab) + 8 bS+ b 2 -(1 R