The rule for finding out the first term and the common ratio in relation to a (given) guņadhana:--
97. The guņadhana 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 guņadhana, 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 guņadhana the number of terms (in the corresponding geometrically progressive series):--
98. Divide the guņadhana (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 division), so much is (the value of) the number of terms in relation to the (given) guņadhana.
Examples in illustration thereof.
99. A certain man (in going from city to city) earned money (in a geometrically progressive series) having 5 dīnāras for the first term (thereof) and 2 for the common ratio. He (thus) entered 8 cities. How many are the dīnāras (in) his (possession) ?
100. What is (the value of) tho 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 arn, when divided by a gives rn ; and this is divisible by r as many times as n, which is accordingly the measure of the number of terms in the series. Similarly r * r * r ... up to n times gives rn; and the guņadhana i.e., arn divided by rn gives a, which is the required first term of the series.
