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Apart from the above formula, methods are given 1. 2. 3. to find the common difference and the first term if the remaining term are known. Quite a good number of examples are also given whose solution by the above formula can easily be done. Three rules giving stanzas for splitting up into the component elements) such as sum of the series in A. P.) as is combined with the first term (af 1997 or with the common difference (उत्तर मिश्रधन) or with the number of terms (गच्छमिश्रधन) or with all these (सर्वमिश्रधन) are given below:
उत्तरधनेन रहितं गच्छेनैकेन संयुतेन हृतम् । मिश्रघनं प्रभवःस्थादिति गणक शिरोमणे विद्धि ।।
"O crest jewel of calculators, understand that misradhana diminished by the Uttardhana and (then) divided by the number of terms increased by one, gives rise to the first term."
Symbolically, if S=sum, a=first term, d=C. D. and n=number of terms then
2
S'_ n (1-1) a = -- --
n+1 Now in the second stanza
where S=S+a.
आदिधनोनं मित्रं रूपोनपदार्धगुणितगच्छेन । सकेन हृतं प्रचयो गच्छविधानास्पदं मुखे सके ।।
"The misradhana diminished by the adidhana, and then divided by the quantity obtained by the) addition of one to the (product of the number of terms multiplied by the half of the number of terms lessened by one (gives rise to the common difference). (In splitting of the number of terms from the misradhana) 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 (so as to cause a corresponding increase in all the terms)".!
lesenthana the crequired number of terms (is obtained in acoma
Algebraically if S=S+d=Uttardhana and na=adidhana then
de
s'- na n(n-1)
+1
1. GSS
GSS GSS
- int no no
8. GSS
माचार्यरत्त श्री देशभूषण जी महाराज अभिनन्दन ग्रन्थ
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