24 GANITASARASANGRAHA. of the number of terms as lessened by the number of terms, (gives) the common difference. The sun (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 multiplied by the half of the number of terms less by one, gives the first term of the series. The common difference is (obtained, when) the sum, divided by the number of terms and then dimi- nished by the first term, is divided by the half of the number of terms less by one. Two rules for finding out, in another way, the common differ- ence and the first term :- 75. Understand that the common difference is (obtained, when) the sum of the series, multiplied by two and divided by the number of terms (therein), is diminished by twice the first term, and is (then) divided by the number of terms lessened by one. 76. Twice the sum of the series divided by the number of terms therein, and (then) diminished by the number of terms as lessened by one and multiplied by the common difference, when divided by two, (gives) the first term of the series. Examples in illustration thereof. 77. The first term is 9; the number of terms is 7; and the sum of the series is 105. Of what value is the common difference? 74. Algebraically, a- 75. Symbolically, b 78. Algebraically, a S 28 n ¹6; and 6 = 2 - 2 a n -1 2 S - (n - 1) b 2 8 - a n n - 1 2
