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" The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient... "
A System of Practical Arithmetic: Applicable to the Present State of Trade ... - Σελίδα 148
των Jeremiah Joyce - 1812 - 258 σελίδες
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Τόμος 1

Samuel Webber - 1801
...ratio. PROBLEM I. Given the first termt the last term, and the ratio, to find tht sum of the series. RULE.* Multiply the last term by the ratio, and from...term, and the remainder, divided by the ratio less I, will give the sum of the series. EXAMPLES. * DEMONSTRATION. Take any series whatever, as i, 3, 9,...

A System of Arithmetic

Samuel Webber - 1812 - 248 σελίδες
...ratio. PROBLEM 1. Given thefirst term, the last term, and the ratio, to find the sum of the series. RULE.* Multiply the last term by the ratio, and from...term, and the remainder, divided by the ratio less 1, will give the sum of the series. * DEMONSTRATION. Take any series whatever, as 1, 3, 9, 27, 81,...

Daboll's Schoolmaster's Assistant: Improved and Enlarged : Being a Plain and ...

Nathan Daboll - 1813 - 240 σελίδες
...The first term, the last term (or the extremes) and the ratio given, to find the sum of the series RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms....

Logarithmick Arithmetick: Containing a New and Correct Table of Logarithms ...

1818 - 251 σελίδες
...Given the first term, the last term, (or extremes') and the ra* t|O, to find the sum of the series, RULE. Multiply the last term by the ratio, and from the product subtract the first term, and the rem ainder, divided by the ratio less I, wjif'give the sum of all the terms of the series. EXAMPLES....

The Scholar's Guide to Arithmetic: Being a Collection of the Most Useful ...

Phinehas Merrill - 1819 - 99 σελίδες
...•Given the first term, the last term, and the ratio, to find the aggregate or total sum of the series. RULE. — Multiply the last term by the ratio, and...divided by the ratio less one, will give the sum of the whole series. EXAMPLES. 1. The first term of a series in geometrical progression is 1 , the last term...

The Youth's Assistant in Theoretick and Practical Arithmetick ...

Zadock Thompson - 1826 - 164 σελίδες
...ratio. Problem I. The Jlnt term, the latt term, and the ratio given to find the turn of the series. RULE.* — Multiply the last term by the ratio, and...term, and the remainder divided by the ratio, less 1, will give the sum of the series. Examples. 1 . The first term of a series in geometrical progression...

The Improved Arithmetic: Newly Arranged and Clearly Illustrated, Both ...

Daniel Parker - 1828 - 348 σελίδες
...stand over the first term, the number oí the exponents must equal the number of terms. PROBLEM I. # RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio less one, and the quotient will be the sum of all the terms....

A Short System of Practical Arithmetic: Compiled from the Best Authorities ...

William Kinne - 1829
...ratio. PROBLEM 1. Given the first term, the last term, and the ratio, to find the sum of the series. RULE. — Multiply the last term by the ratio, and...term, and the remainder divided by the ratio less 1, will give the sum of the series. EXAMPLES. 1 . The extremes of a geometrical progression are 1 and...

Daboll's Schoolmaster's Assistant: Improved and Enl. ...

Nathan Daboll - 1829 - 240 σελίδες
...The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms....

Connolly's Arithmetic: Or, The Ohio Accomptant: Being a Plain Practical ...

James L. Connolly (mathematician.) - 1829 - 250 σελίδες
...first term, the last term, or the extremes, and the ratio, given to find the sum of the series. RULK 1. Multiply the last term by the ratio, and from the product subtract the first term; then divide the remainder by the ratio less one, and the quotient will be the sum of all the terms....




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