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CHAPTER II-ARITHMETICAL OPERATIONS.
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The rule for finding out, from the known rum, first term, and common difference of a given is in arithmetical progression), the first term and the commons terence (of auotlr sories), the optionally chosen sum (whereof) is wice, throe Ames, half, onethird, or sone such (multiple or fraction of the known sum of the given series):- .
84. Put down in two places for facility of working) the choson sum as divided by the known vie., the given) sum; this (quotient) whou multiplied by the (known) corumou difference gives the required) common difference; and that (name) quotient when multiplied by the (known) first torm gives the required) first term of the series of which the sum is cither a multiple or a fraction of the known sum of the given series)
Eramples in illustration the rol. 85. Sixty is the (known first term, and the known) common difference is twice that, and the number of forms in the sume, 1.m., 4 (in the giveu scries is well as in all the required series). Give out the first terms and the common differences of these required (series, the sums whereof are) represented by that (known sum) as multiplied or divided by the (number) beginning with 2.
The rule for finding ont, in relation to two (ories, the number of terms wherein are optionally whore'n, their mutually interchangod first term and common difference, it also their name whicb . may be cqual, or (one of which may be) twice, thrice, hall, or onethird, or any such (multiple or fraction of the other) :
86. The number of terins in one horios), multiplied by itself as lessened by me, and then multiplied by the chosen (ratio between the sums of the two Horics), and then diminished by
Rek. Symbolically, as = ša, l's
1,w.rw. ;. ", und long nor the am, thin
Arst torm and the common difference, in order of the mories whomum in chromon. Given the of two vericu, the ratio between the two firnt terms and that between the dommon differences need not alwaye bwa The wolution here given in hence plicablo only to curtain particular casen.
86. Algebraio ly, a - *(n-1) - 2n, and I, () - -2pn, whoro a, b and are the first term, the common difference and the number of
