________________
GOMMATASARA.
43
is even, then, it is half the sum of the two middle or the two extreme terms. It is found by adding together the first and the last term and dividing by 2.
7. The number of terms multiplied by the first term gives the Adi-dhana (Ha).
8. The number of terms minus one, multiplied by the common difference gives the Chaya-dhana.[n-1(d.]
9. Half the number of terms, multiplied by Chaya-dhana, gives the Uttara-dhana (((n-1) d.]
10. The sum of Ádi-dhana and Uttara-dhana is Sarva-dhana.
Thus.
na + ” (1. – 1)d. - {2a+ in-1)d}
"{a+ (n-1d + a} =?: (a +1)
=n. 471-s. 11. Half the sum of the 1st and the last terms multiplied by the number of terms-Sum. Sanx(+)
12. Number of terms or Gachchha - (difference between the last and the first terms divided by the common difference +1)
*
+1.
13. Divide the sum by the number of terms; from the quotient subtract the first term ; divide the remainder by the number of terms -1; the result will be half the common difference.
14. From the sum subtract the Adi dhana, divide the remainder by the number of terms, then divide the quotient by the number of terms -1, the result will be of the common difference.
d.- s-na
n (1- 1)
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