32 GANITASĀRASANGRAHA. 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 certain quantity in which (product) that (quantity) occurs as often as the number of terms (in the series); and this (quantity) is the (required) common ratio The gunadhana, when divided by that (self-multiplied) product of the common ratio in which (product the frequency 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, (each representing a single such divi- sion), so much is (the value of) the number of terms in relation to the (given) gunadhand. Examples in illustration thereof. 99. A certain man (in going from city to city) earned money (in a geometrically progressive series) having 5 dināras for the first term (thereof) and 2 for the common ratio. He (thus) entered 8 cities How many are the dinaras (in) his (possession)? 100. What is (the value of) the wealth owned by a merchant (when it is measured by the sum 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 98. It is clear that an, when divided by a gives r", and this is divis- ible by r as many times as n, which is accordingly the measure of the number of terms in the series. Similarly rx rx.. up to times gives", and the gunadhana t.e., ar divided by this r gives a, which is the required first term of the series.
