________________
JAINA ANTIQUARY.
[Vol. I
23, 24, 212, ..., 28.9"-?....
(14) Dvirūpaghanāghana-dhārā,
83, 86, 812,...
or
2
1-1
3
• 2
29, 218, 236, ..., 2 The subject of series is stated to have been treated comprehensively in a special treatise entitled Vrhaddhārāparikarma ("Great Treatise on the Operations of Series"). Nemicandra has referred his more enthusiastic readers to :that treatise for fuller informations on the subject, he having noted only a small portion of it suital le foi his practical purpose. No such treatise is available now. It is
lost.
Arithmetical Progression. Nemicandra says:
** Multiply the number of terms as diminished by unity by the common difference. The product added with the first term gives the last term, and when subtracted from the last term yeilds the first. Half the sum of the first and last terms multiplied by the number of terms becomes the sum of the seri es."2
Let a=the first term, l=the last term, b=the comř on difference, n=the number of terms and Sn = the sum of a series in arithmetical progression ; then the rule says,
l=a+(n-1)6, a=1-(n-1)0
Sn=" (a +l). “The number of terms is diminished by unity and then divided by two and multiplied by the common difference. Add the result to the first term and multiply the sum by the number of terms. Know the product to be the sum of the series."
8. =n{a + (47) };
1Trilokasāra, Gāthā 91,
2 Ilid, Gāthā 163.
3 Ibid, Gāthā 164.
