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GANITASĀRASANGRAHA.
difference. (In splitting up the namber of terms from the miéradhana), the (required) number of terms (is obtained) in accordance with the rule for obtaining the number of terms, provided that the first term is taken to be increased by one (80 as to cause a corresponding increase in all the terms).
82. The misradhana is diminished by the first term and the number of terms, both of those) being optionally chosen; (then) that quantity, which is obtained from this difference) by applying the rule for (splitting up) the uttora-misradhana, happens to be the common differenco (required here). This is the mathod of work in (splitting np) the all-combined (mirulhana).
Scamples in illustration thereof. 83. Forty exceeded hy 2, 3, 5 and 10, represonts (in order) the adi-mikrauthanul and the other (mirathanax). Toll me what (respeotively) happens in these cases to be the first term, the common difference, the number of terms and all (these three).
serios in urithmetical progression. There are accordingly four different kinds of mifradhava mentioned hero; and they are respectively adi-migrudhana, wtura. mitrachana, yaccha-nisradhana and sarva-nisradhana. For adidhana and uttara. Ihana noo noto under stanzas 63 and 6 in this chapter.
Sa-
(n-1)
2
+
whore
Algebruicully, stanza 80 works out thus : a = _So is the adi-misradhana, i.e., 8 + a.
80 - ma where So is the uttura-mibradhaga, And stanza 81 giver b = 32
(n-1)+1
1.6., 8 +0: and further points out that the value of may be foun out, when the value of $n, which, being the gaccha-miúradhanu, it equal to $ + , in given, from the fact that, when S a + (a + b) + (a + 2b) + ...up tan terms, Sn = (a + 1) + (a + 1 + b) (a + 1 + 21)
+ ..... up to the same n terms. Simco, in stanza 82, the choice of u and n aro left to our option, the
problem of finding out a, m, and l from the given value of Sand. which, being the marva. misradhana, is oyual to 8 + 0 + + + b, resolves itself canily to the finding out of 5 from any giveu value of St in the
manner above explained. 83. The problom expressed in plainer terms is :-(1) Find out a when &a = 42, b=3 and 5. (2) Vind out b, when 80 = 43, q=2 and 5. (3) Find out
when S + - 3, 4 * 2 and b 3. And (4) find out a, b, and when 3 + 4 + 0 + = 50,
