 | William Smyth - 1833 - 288 σελίδες
...we may obtain the sum of any number of the terms of a progression by quotient ; for this purpose, we multiply the last term by the ratio, subtract the...divide the remainder by the ratio diminished by unity. Let it be required to find the sum of the first 4 terms of the progression 4-- 2 : 6 : 18 : 54 : 162,... | |
 | Francis Joseph Grund - 1833 - 224 σελίδες
...obtain the sum of all the terms of a Geometrical Progression multiply the quotient by the last term, subtract the first term from this product, and divide the remainder by the quotient diminished by unity. APPLICATIONS. 1) The first term is 1 ) What is the 7th term, the Quotient... | |
 | 1838 - 372 σελίδες
...S, Sa=(Sl)q=Sq-lq, or Sq-S=lq—a; la — a whence S=— — — . That is, to obtain the sum of the terms of a progression by quotients, multiply the...divide the remainder by the ratio diminished by unity. 1. Find the sum of eight terms of the progression 2 : 6 : 18 : 54 : 162 . . . : 2x37=4374, 2. Find... | |
 | Charles Davies - 1842 - 368 σελίδες
...S—a=(S—l)q=Sq—Iq, or Sq—S=lq—a-, whence S=———. f-1 That is, to obtain the sum of the terms of a progression by quotients, multiply the...divide the remainder by the ratio diminished by unity. 1. Find the sum of eight terms of the progression 2 : 6 : 18 : 54 : 162 . . . : 2x3 7 =4374, 2. Find... | |
 | Thomas Sherwin - 1842 - 326 σελίδες
...terms, multiply the remainder by the first term,, and divide the product by the ratio minus unity ; or, multiply the last term by the ratio, subtract the first term from the product, and divide the remainder by the ratio minus unity. Ex. Required the sum of the series,... | |
 | Charles Davies - 1845 - 382 σελίδες
...1 and by substituting for orn, its value Ir, we have s_lr-a -T^TT That is, to obtain the sum of any number of terms of a progression by quotients, multiply...divide the remainder by the ratio diminished by unity. EXAMPLES. 1. Find the sum of eight terms of the progression 2 : 6 : 18 : 54 : 162 . . . : 2 X 37 =... | |
 | Frederic A. Adams - 1846 - 230 σελίδες
...last terms are given, and the ratio, RULE. — Multiply the last term by the ratio, subtract thejirst term from this product, and divide the remainder by the ratio diminished by one. 5. A gentleman promises his son, 11 years old, one mill when he shall be 12 years old, and, on... | |
 | William Smyth - 1847 - 276 σελίδες
...sum of any number of the terms of a progression by quotient ; for this purpose, we multiply the latt term by the ratio, subtract the first term from this...divide the remainder by the ratio diminished by unity. Let it be required to find the sum of the first 4 terms of the progression --f 2 : 6 : 18 : 54 : 162,... | |
 | 1847 - 386 σελίδες
...and by substituting for arn, its value Ir, we have Ir -a S = r-1 That is, to obtain the sum of any number of terms of a progression by quotients, multiply the last term by the ratio, subtract the ßrst term from this product, and divide the remainder by the ratio diminished by unity. EXAMPLES.... | |
 | James Robinson (of Boston.) - 1847 - 304 σελίδες
...when we have the first term and ratio given. RULE. Find the last term by the rule in Art. 179, then multiply the last term by the ratio, subtract the first term from the product, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of all the... | |
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... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity. 
