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" That is, the last term of a geometrical progression is equal to the first term multiplied by the ratio raised to a power whose exponent is one less than the number of terms. "
Elements of Algebra - Page 190
1838 - 355 pages
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A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

Charles Hutton - Astronomy - 1815 - 686 pages
...uneven number of the terms. 2, 4, 8, 16, 8421 ti ~Гб Thus, prod. Also prod 1, 16 T , 16 ra. 3. The last term of a geometrical progression, is equal to the first term multiplied, or divided, by the ratio raised to the power whose exponent is less by 1 than the number of terms in...
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...= bq = aq', d = cq = aq3 from which it will be readily inferred, that a term of any von A whatever is equal to the first term multiplied by the ratio raised to a power, the exponent of which is one less than the number, which marks the place of this term. Let L designate...
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The Common School Arithmetic: Prepared for the Use of Academies and Common ...

Charles Davies - Arithmetic - 1833 - 284 pages
...2=24 4th term, &c. for the other terms. But 2x2=23,2x2x2=23, and 2x2x2x2=2*. Therefore, any term of a progression is equal to the first term multiplied by the ratio raised to a power" 1 less than the number of the term. CASE I. 230. Having given the first term, the common ratio,...
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Mental and Practical Arithmetic

Charles Davies - Arithmetic - 1838 - 292 pages
...term, &c. for the other terms. But2x2 = 22, 2x2 x 2 = 23, and 2x2x2x2=2*. Therefore, any term of the progression is equal to the • first term multiplied by the ratio raised to a power 1 less ' than the number of the term. Q. In every Geometrical Progression, how many things are considered?...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 272 pages
...which has n — 1 terms before it, is expressed by aq"~l. Let / be this term ; we then have the formula by means of which we can obtain any term without being obliged to find all the terms which precede it. Hence, to find the last term of a progression, we have the following RULE. I. Raise the ratio to a...
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A New System of Arithmetic: In which is Explained and Applied to Practical ...

Calvin Tracy - Arithmetic - 1840 - 316 pages
...3, 3 is evidently to be taken as multiplier, or factor, eleven times ; that is, any term of a series is equal to the first term multiplied by the ratio raised to a power one less than the number of terms. Thus, 2 x 3 x 3 x 3x3x3x3x3x3x3x3x3" = 3x2= 354294, Ans-. or twelfth...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...n—1 terms before it, is expressed by aq"- l . Let Z be this term ; we have the formula l=aq*- i , by means of which we can obtain any term without being...term of a geometrical progression is equal to the f,rst term multiplied by the ratio raised to a power whose exponent is one less than the number of...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 pages
...n— 1 terms before it, is expressed by af~l. Let l be this term ; we then have the formula l=aq-\ by means of which we can obtain any term without being obliged to find all the terms which precede it. Hence, to find the last term of a progression, we have the following RULE. I. Raise the ratio to a...
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Arithmetic, designed for academies and schools, with answers

Charles DAVIES (LL.D.) - Arithmetic - 1843 - 348 pages
...4th term, &c. for the other terms. But 2x2=22, 2x2x2=23, and 2x2x2x2=2*. Therefore, any term of the progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term. Q. In every Geometrical Progression, how many things are considered...
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Arithmetic Designed for Academies and Schools: With Answers

Charles Davies - Arithmetic - 1844 - 666 pages
...4th term, &c. for the other terms. But 2x2=22, 2x2x2=23, and 2x2x2x2=24. Therefore, any term of the progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term. Q. In every Geometrical Progression, how many things are considered...
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