GANITASĀRASANGRAHA. The rule for finding out the number of terms in a geome- trically progressive series :- 103. Multiply the sum (of the given series in geometrical progression) by the common ratio lessened by one; (then) divide this (product) by the first term and (then) add one to this (quotient) The number of times that this (resulting quantity) is (successively) divisible by the common ratio-that gives the measure of the number of terms (in the series). 34 Examples in illustration thereof. 104. O my excellently able mathematical friend, tell me of what value the number of terms is in relation to (a series, whereof) the first term is 3, the common ratio is 6, and the sum is 777. 105. What is the value of the number of terms in those (series) which (respectively) have 5 for the first term, 2 for the common ratio, 1275 for the sum: 7 for the first term, 3 for the common ratio, 68887 for the sum: and 3 for the first term, 5 for the common ratio and 22888183593 for the sum ? Thus ends summation, the seventh of the operations known as Parikarman. Vyutkalita. The rule of work in relation to the operation of Vyutkalta,* which is the eighth (of the Pariharman operations), is as follows:- 106. (Take) the chosen-off number of terms as combined with the total number of terms (in the series), and (take) also your own chosen-off number of terms (simply); diminish (each of)
- In a given series, any portion chosen off from the beginning is called sta
or the chosen-off part; and the rest of the series is called ś7 a, and it contains the remaining terms and forms the remainder-series. It is the sum of these s sa terms which is called vyutkaista. 106. Algebraically, vyutkalta or Sv=== + d-1 sum of the ista or S= the chosen-off part of the series. = ( ² = ¹.6 .6 + b + a }(n-d), and the d; where d is the number of terms in
