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CHAPTER II --ARITHMETICAL OPERATIONS.
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of) this operation) is diminishod by one, and (is thon) multiplied by the first term, and is then) divided by the common ratio lessened by one, it becomes the snm (of the series).
The rule for finding out the last term in a goonetrically progressivo series as also the sum of that (sories) :
95. The antyadhana or the last term of a series in geometrical progression is the yumuidhiana (of another sories) wheroin the number of terms is less by me. This (antyodhana), whon multiplied by the common ratio, aud (then) diminishod by the first term, and (thon) divided by the common ratio lessened by one, gives rise to the sum of the sorios).
An crample in illustration thereof. 96. Having (first) ohtnined 2 golden coins (in some wity), a man goes on from oity to city, carning (overywhere three timos (of what he carned immediately before. Say how much he will make in the eighth city.
Now, in the representative column of figuras derived and given in tho margin
o the lowest 1 in multiplied by r, which giver since this lowest I haw 0 above it, thu robinet before in ured, which gives wince this 0) i ham ) above it, the now btained is multiplied by r, which gives mi 0 wince this I har 0 above it, this in nuured, which gives': And Ninco I again this has another above it, this in nurod, wluch gives
Thus the value of why be arrived at ly uning n bow time is powmible the proceMON of qualing and imple multiplication. The object of the method in to facilitate the ditermination of the value of dit in early on that tho method hold true for all positive and integral values of ..
ar ixra 95. Exprowned algebraically, $ : ". " The antyathunu In the value of the last termin # mereu in krometrien progression for tho meuning and value of yunadhana, za %3 above in this chapter. The antyadhana of geometrically progressive series of n terminal, while the annadhana of the same nerica in ar". Similarly the antywland of geometrically progressive series of n - 1 terus in ar" , while the adhama thurwol in arr-, Here it in ovident that the antyalhana of the worin of terms in the mamo the qunadhana of the sering of -1 terme.
