An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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... Arithmetical Progression . II . Geometrical Progression . · 186 186 195 18 CHAPTER VIII . GENERAL THEORY OF EQUATIONS . SECTION I. Composition of Equations . II . Equal Roots . III . Real Roots . on 201 he 201 en · 210 214 el CO CHAPTER ...
... Arithmetical Progression . II . Geometrical Progression . · 186 186 195 18 CHAPTER VIII . GENERAL THEORY OF EQUATIONS . SECTION I. Composition of Equations . II . Equal Roots . III . Real Roots . on 201 he 201 en · 210 214 el CO CHAPTER ...
Page 186
... Arithmetical Progression . 244. An Arithmetical Progression , or a progres- sion by differences , is a series of terms or quantities which continually increase or decrease by a constant quantity . This constant increment or decrement is ...
... Arithmetical Progression . 244. An Arithmetical Progression , or a progres- sion by differences , is a series of terms or quantities which continually increase or decrease by a constant quantity . This constant increment or decrement is ...
Page 187
... arithmetical series , is equal to the sum of the two extremes . 249. Problem . To find the sum of an arithmeti- cal progression when its first term , last term , and number of terms are known . Solution . In this case , a , l , and n ...
... arithmetical series , is equal to the sum of the two extremes . 249. Problem . To find the sum of an arithmeti- cal progression when its first term , last term , and number of terms are known . Solution . In this case , a , l , and n ...
Page 189
... 7 and n , when a , r , and S are known . Ans . n = √ [ 2 r S + ( a — } r ) 2 ] — ( a — } r ) , r l = √ [ 2rS + ( a — { r ) 2 ] — } r . Examples in Progression . 11. Find the last term and CH . VII . § I. ] ARITHMETICAL PROGRESSION . 189.
... 7 and n , when a , r , and S are known . Ans . n = √ [ 2 r S + ( a — } r ) 2 ] — ( a — } r ) , r l = √ [ 2rS + ( a — { r ) 2 ] — } r . Examples in Progression . 11. Find the last term and CH . VII . § I. ] ARITHMETICAL PROGRESSION . 189.
Page 191
... of numbers from 1 to 100 . Ans . 5050 . 24. Find the sum of the odd numbers 1 , 3 , 5 , & c . up to n terms . Ans . n2 . Examples in Progression . 25. Find the sum of the CH . VII . § I. ] ARITHMETICAL PROGRESSION . 191.
... of numbers from 1 to 100 . Ans . 5050 . 24. Find the sum of the odd numbers 1 , 3 , 5 , & c . up to n terms . Ans . n2 . Examples in Progression . 25. Find the sum of the CH . VII . § I. ] ARITHMETICAL PROGRESSION . 191.
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence