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36
GANITASĀRASANGRAHA.
Tho rule for finding out the first term in relation to the remaining number of terms (bolonging to the remainder-series) :
109. The chosen-off number of terms multiplied by the common difference and thon) combined with the first terin (of the given series) gives rise to the first term in relation to the remaining terms (belonging to the remainder-series) " he already mentioned common differonco is the common difference in relation to these (remaining torms also); And in relation to the choseu-off number of terms (also both the first term and the common difference) are exactly those (which are found in the given series).
The rule for finding out the first term in relation to the remaining number of terms belonging to the remainder-series in a goometrically progressive series :
110. Even in respect of a geometrically progressive series, the cominon rati) and the first term ar exactly alike in the given serios and in the chosen-off part thereof). There is (however) this difference bere in respect of the first term in relation to the remaining number of torms (in the remainder-serios), viz., that the first term of the 'givon) series multiplied by that self-multiplied product of the common ratio, in which (product) the frequency of the occurrence of the common ratio is measured by the chosen-off number of teims, gives rise to the first term of the remainder-series)
. Examples in illustration thereuf. 111. Calculate what the sums of the remainder-sorios are in rospect of a series in arithmetical progression, the first term of which is 2, the common difference is 3, and the number of terms is 14, when the chosen-off numbers of the terms are 7, 8, 9, 6 and 5 (respectively).
112. (In conuection with a series in arithmetical progression) here (given), the first term is 6, the common difference is 8, the number of torms is 36, and the chosen-off numbers of turms are 10,
109. The first term of the remainder series = db + a. The series dealt with in this rulo is obviously in arithmetical progression
. 110. The first term of the remainder series is art.
