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OHAPTER 11 - ARITHMETICAL OPERATIONS.
The common difference (in respect of another series) is 5, the number of terms is 8, and the sum is 15€. Tell me the first term.
The rule for finding out how (wben the sum is given) the first term, the common difference, and the number of terms may, as desired, be arrived at :
78. When the sum is divided by any chosen number, the divisor becomes the number of terms (in the series); when the quotient here is diminished by any number chosen (again), this subtracted number boomes the first term (in the porics); and the remainder (got after this subtraction) wheu divided by the half of the number of terme lessoned by one becomes the common difference.
Example in illustration therrul. 79. The sun given in this problem in 540. () crest-jowel of arithmeticians, tell me the number of terms, the common difforence, and the first term.
Three rule-giving stanzas for splitting up into the component elements such a sum of a series in arithmetical progression) as is combined with the first torm, or witb the common differences, or with the number of terms, or with all thehe.
80 () errost-jewel of calculators, understand that the misraithana diminished by the uttarudita, and (then) divided by the number of terms to which one has been added, gives rive to be first torm.
. 81. The wirudhawl, criminished by the w hana, and (then) ilivided by the quantity obtained by the) aldition of me to be
product of the number of terms multiplied by the half of tho number of turmus lossened by www. (gives rise to the common
78. Symbolically, the problem herein is to find out when Min kiven, and a and are allowed to be chosen loption. Naturally, there may be in solution to any given value of Sony values of b, which went on the chosen value of a and . When the values of and re delinitely chon, the rule heroin kiven for finding onto turn out to be the ramuri lat niven in Mtunan 74 v.
40-82. The expression inadhara mak #mixed num. Itin used here to depote the quantity which may be obtained by adding the first
t o the common difference or the number of termin or a thire of these to the sum of
