The Arithmetical Expositor, Or, A Treatise on the Theory and Practice of Arithmetic: Suited to the Commerce of the United States : in Two Parts, Volume 1Kimber and Sharpless, 1824 - Arithmetic |
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Page 5
... numbers are such , that the difference be- tween the first and second is ... Given , the number of terms , the common difference , and one of the ... numbers . I have retained the term arithmetical progression in compliance with general ...
... numbers are such , that the difference be- tween the first and second is ... Given , the number of terms , the common difference , and one of the ... numbers . I have retained the term arithmetical progression in compliance with general ...
Page 6
... number of terms , multiply the remainder by the common difference ; the product added to , or subtracted from , the given extreme , according as the less or greater is given , will produce the required extreme . Half the sum of the ...
... number of terms , multiply the remainder by the common difference ; the product added to , or subtracted from , the given extreme , according as the less or greater is given , will produce the required extreme . Half the sum of the ...
Page 7
... number of terms 21 ; required the less extreme , and sum of the series ? Ans . less extr . 10 , sum 140 . CASE 2 . Given , the two extremes and number of terms to find the common difference ? RULE . Subtract a unit from the number of ...
... number of terms 21 ; required the less extreme , and sum of the series ? Ans . less extr . 10 , sum 140 . CASE 2 . Given , the two extremes and number of terms to find the common difference ? RULE . Subtract a unit from the number of ...
Page 10
... Given the first term 1 , ratio , and number of terms 21 , to find the sum of the series . Result 14743392200 4401 ... numbers 89 and 87 may be taken from the table , page 123 , Part I , and hence the answer be obtained by one ...
... Given the first term 1 , ratio , and number of terms 21 , to find the sum of the series . Result 14743392200 4401 ... numbers 89 and 87 may be taken from the table , page 123 , Part I , and hence the answer be obtained by one ...
Page 11
... Given the less extreme 2 , the greater 1062882 and the number of terms 13 ; required the ratio ? Ans . 3 . HARMONICAL PROGRESSION . Three numbers are said to be in harmonical propor- tion , when the first has to the third , the same ...
... Given the less extreme 2 , the greater 1062882 and the number of terms 13 ; required the ratio ? Ans . 3 . HARMONICAL PROGRESSION . Three numbers are said to be in harmonical propor- tion , when the first has to the third , the same ...
Common terms and phrases
aliquot ARITHMETICAL EXPOSITOR ARITHMETICAL PROGRESSION bushel carats ciphers CIRCULATING DECIMALS circulating figures common difference compound interest contained debt denominator denote digits dividend divisor equal equation equidifferent numbers equidifferent series equivalent vulgar fraction EXAMPLE 12 extremes find the present finite decimals fourth term geometrical means GEOMETRICAL PROGRESSION given numbers given to find harmonical mean Hence ingredients interest being reckoned last term less minuend mixed multiple of 9 multiplicand multiply the annuity nuity number of combinations number of terms numbers found obvious ounces payable yearly permutations perpetuity piastres pound present money present value present worth prices or qualities prime numbers proper fraction proper numbers proposed rate quotient rate of interest rate per cent remainder repeating or circulating repetend or circulate Required the present result right hand figure root RULE OF THREE second term series of numbers subtract suppose tabular number third term unit whence yards
Popular passages
Page 2 - An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the time therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and...
Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 2 - An Act supplementary to an Act, entitled, " An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts, and Books, to the Authors and Proprietors of such Copies during the times therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
Page 8 - Hence, the first term, ratio, and number of terms being given, to find the sum of the series, RULE. Raise the ratio to a power whose index is one less than the number of terms, from which subtract 1, and divide the remainder by the ratio less 1 ; the quotient is the sum of a series with 1 for the first term; then multiply this quotient by the first term of any required series ; the product will be its amount.
Page 5 - If we have four numbers, 2, 4, 8, and 10, of which the difference between the first and second is equal to the difference between the third and fourth, these numbers are said to be in arithmetical proportion. The first term 2 is called an antecedent, and the second term 4, with which it is compared, a consequent. The number 8 is also called an antecedent, and the number 10, with which it is compared, a consequent.
Page 64 - That is, the first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one.
Page 43 - ... be. RULE. Take a series proceeding from and increasing by a unit, up to the number to be combined ; and another series of as many places decreasing by a unit, from the number out of which the combinations are to be made, multiply...
Page 7 - If the extremes be 10 and 70, and the number of terms 21 ; what is the common difference, and the sum of the series ? Ans. th
Page 70 - There will dx also be n — m constants in the resulting equation ; and as we can choose at pleasure the m constants we eliminate, we can form as many resulting equations containing n — m constants, as the number of combinations that can be formed out of n things taken »г at a time ; that is, n (n — 1) ... (n — m + 1) [m.
Page 8 - Multiply the last term by the ratio, and divide the difference between this product and the first term by the difference between the ratio and one.