required series) is (taken to be) . The sum of the required series is of the same value ). Find out, O friend, the first term and the common difference (of the required series).
31. The first term is twice the common difference (which is taken to be 1); the number of terms is (taken to be). The sum of tho required series is . Find out the first term and the common difference.
82. The first term is 1, the common difference is and the number of terms common (to both the given as well as the required series) is (taken to be) . The sum of the required series is . Give out the first term and the common difference (of the required series).
The rule for finding out the number of terms (in a series in arithmetical progression):-
38. When, to the square root of (the quantity obtained by) the addition, of the square of the difference between the half of the common difference and the first term, to twice the common difference multiplied by the sum of the series, half the common difference is added, and when (this sum is) diminished by the first term, and (then) divided by the common difference, (we get) the number of terms in the series.
He (the author) states in another way (the rule for finding out) the same (number of terms):--
34. When, from the square root of (the quantity obtained by) the addition, of the square of the difference between the half of the common difference and the first term, to twice the common difference multiplied by the sum of the series, the kşēpapada is subtracted, and when (this resulting quantity is) divided by the common difference. (we get) the number of terms in the series.
33. Symbolically expressed, . Cf. note under 69, in Chap. II
34. For kşēpapada, see note under 70 in Chap. II
