358 Journal of the Asiatic Society of Bengal. (September, 1912. 
Sttra 18. If two arithmetical proenenaions of the same 
number of terms (n) have equal sums 
a S11 and gam (2a+n—1 1.d) 
ghar aa 3 

where a,, a, are the initial terms, d, and d, the common differ- 
ences. 
Example 1. 
First terms 2 and 3, increments 3 and 2, n= 3, ¢=16. 
Example 2 
First terms 5 and 10, increments 6 and 8, n= 41, = 66. 
Progressions are treated in all Hindu works. Mahavira 
8 
n—1 
a, = —5— (dg —d}) +a, 
but makes a,=1. Bhaskara gives no such rule, 
Sitra Having subtracted the series (of rates) and the 
multiplication of the instalments from one, determine the 
original amount by multiplication after dividin ng. 
Example :—A merchant Pays octroi (in kind) on certain 
goods at three different plac At the first he gives 5 4 of the 
goods, at the second he aire 4. 4, ‘and at the third 2. The total 
tomy of duty paid is 24. What is the original amount of the 
go 
Fee 
1~(1-3)1-3)01=4) 
There are three other examples given. om ve gives ! 
an example a to the above. It i t is as f allow ows 
The solution is =40. Answer. 
with which he returned home. T ell me the amount of his stock 
of money if me have learned the method of reduction of frac- 
tions of residues 
j 63 
Solution LASERS RSI Ne 
Aelia uae ees ar: 
1 Lilavati, § 53 
