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CHAPTER III-PRACTIONS.
47
divided ty the common ratio lessened by one, gives rise to the sum (of the series)
ottes).
An example in illustration thereof. 42. In relation to a serios in geometrical progression, the first term is t, the common ratio is and the number of terins is hero 5. Tell me quickly the sum and the last term of that (sories).
The first term, the common ratio and the number of terms, in relation to the gunadhana and the sum of a series in geometrical progression, abould also be found out by means of the rules utatod already in the last chapter).*
The rule for finding out the common) first term of two serios having the saine sum, ono of them being in arithmetical progression and the other in geometrical progression, their optionally oboson number of terms being equal and the similarly chosen common difference and common ratio also being oqual in value.
43. One is taken as the first term, the numbor of torms and the cominon ratio as well as the common difference (which is equal to it) are optionally choson. The uttaradhana (bero), divided by the sum of this geomotrically progressive series Hy diminished by the adidhana (thercof), and (then) multiplied by whatever is taken as the first term, gives rise to tho (required common) first term in relation to the two sories, (one of which is in goometrical progrosion and the other in arithmetical progression, and both of) wbich are characterised by sums of the same value,
. For those ralen, nce 87, 94, 101 and 103, Chap. II. 43. For ddidhana and uttardhana, noc note onder 03 and 64, Ch. II. This
rule, ayrubolically expressed, works ont thus : a = -
wlore
=
(
-1)
Por facility of working, 1 is chosen as the provisional first term, but it is obvious that any quantity may be no provisionally choren. The one of the provisional Brat term is seen in facilitating the statement of the rule by means of the expressions ddidhana und wftaradhawi. The formula bere given in obtained by equating the formulw kiving the sume of the krometrical and the arithmetical series. It is worth noting that the word caya ig und bere to denoto both the common difference in an arithmetical spd the common ratio in a geometrical weries,
