________________
32
GANITABARASANGRAHA.
The rule for finding out the first term and the common ratio in relation to a (given) gunadhana :
97. The gunadhana when divided by the first term becomes equal to the self-multiplied) product of a «ertain quantity in which (product) that (quantity) occurs as often as the pumber of terms (in the series); and this (quantity) is the required) common ratio. The gunadhana, when divided by that (self-multiplied) produot of the common ratio in which (product the frequenoy of the occurrence of this common ratio) is measured by the number of terms (in the series), gives rise to the first term.
The rule for finding out in relation to a given gunadhana the number of terms in the corresponding geometrically progressive series) :
98. Divide the yunadhana (of the series) by the first term (thereof). Then divide this (quotient) by the common ratio (time after time) so that there is nothing left (to carry out such a division any further); whatever happens here) to be the number of vertical strokes, (oach representing a single such division), so much is the value of the number of terms in relation to the (given) gunadhana.
Examples in illustration thereof. 99. A certain man (in going from city to city) carned money (in a geometrically progressive series) having 5 linärus for the first term (thereof) and 2 for the common ratio. Ho (thus) entered 8 cities. How many are the dinarax (in) his (possession)?
100. What is the value of) the wealth owned by a merchant (when it is ineasured by the sun of a geometrically progressive series), the first term whereof is 7, the common ratio 3, and the number of terms (wherein) is 9: and again (when it is measured by the sum of another geometrically progressive series), the first
97 and 88. It is clear that ar, when divided by a given : And this is disia. iblo by as many times AA #, which is accordingly the measure of the number of terms in the norius. Sirailarly r *r*?...... up to times gives r*; and the gunadhana i.e., ar divided by this rgives a, which is the required first terin of the series.
