________________
24
GANITASARASANGRAHA.
of the number of terms as lessened by the number of terms, (gives) the common difference. The sum (of the series) diminished by uttaradhana and (then) divided by the number of terms, (gives) the first term of the series,
The rule for finding out the first term as well as the common difference :--
74. The sum of the series divided by the number of terms (therein), when diminished by the product of the common difference d by the half of the number of terms less by one, gives when) the sum, divic series. The common difference is (obtained, uished by the first ternt by the number of terms and then dimiterms less by one. is divided by the half of the number of
Two rules for finding out, i ence and the first term:
nother way, the common differ
75. Understand that the common a li the sum of the series, multiplied by ifference is (obtained, when) number of terms (therein), is diminished by and is (then) divided by the number of terms lessened by one. fo and divided by the twice the first term,
76. Twice the sum of the series divided by the enumber of terms therein, and (then) diminished by the number of gs terms as lessened by one and multiplied by the common differeno 4 divided by two, (gives) the first term of the series. when
0,
Examples in illustration thereof.
in
77. The first term is 9; the number of terms is 7; and the sun. of the series is 105. Of what value is the common difference?
74. Algebraically, a
75. Symbolically, b
76. Algebraically, a
8
21
2S
"
#
28
21
21
1
2 b; and b =
- 2 a
- (n-1) b
2
S
"
-a
N-1 2
