Deshbhushanji Aacharya Abhinandan Granth

SR No.: 012045
Original Sutra Author: N/A
Author: R C Gupta
Publisher: Deshbhushanji Maharaj Trust
Publication Year: 1987
Total Pages: 1766
Language: Hindi, English
Classification: Smruti_Granth & Articles
File Size: 56 MB

Page 932

"The number of terms (in one series), multiplied by itself as lessened by one and then multiplied by the chosen ratio between the sums of the two series, and then diminished by twice the number of terms in the other series gives (rise to the interchangeable) first term of one of the series). The square of the (number of terms in the other (series) diminished (again) by the product of two (times the) chosen (ratio) and the number of terms in the first series) gives (rise to the interchangeable common difference of that series)."
Symbolically if S, S, be the sums, a, a, the first terms and d, d, the common differences of the two given series ther
I and n, n, be the respective number of terms in the two series, then according to the above formula
a=n(n-1) Xr-2n, and
d=(n)-1, -2rn
Example:
पंचाष्टगच्छउँसोय॑स्तप्रभवोत्तरे समानधनम् ।
द्वित्रिगुणादिधनं वा ब्रू हि त्वं गणक विगणय्य ।। "In relation to two men (whose wealth is measured) respectively by the sums of two series in A.P. having 5 and 8 for the number of terms, the first term and the common difference and both these series be interchangeable (in relation to each other), the sums (of the series) being equal or the sum (of one of them) heing twice. thrice, or any such (multiple of that of the other), 'O arithmetician, give out the (value of these) sums and the interchangeable first term and common difference after calculating them all) well." Solution : If S=S, then r=1 so in the above case where n=5 and 1,8 we have
a=n(n-1) X 1 --- 2n =5 (5-1) X1-2 x 8 = 20 - 16 = 4
and
d= (0)" - D
- 2 rn
= (8)2 -- 8 - 2X1 X5= 64 - 8 -- 10 - 46
Then
s={(2 x 4 +5–1) x 46) = 5(4+92) = 480
and
S=(2 x 46+ (8–1) 4)=419 +28) – 480
which proves that
1. GSS 2
27
87
आचार्यरत्न श्री वेशभूषण जी महाराज अभिनन्दन ग्रन्थ