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Hence, the sum of a series of numbers in progression by difference is one half of the product of the number of terms by the sum of the first and last terms.
An Introduction to Algebra Upon the Inductive Method of Instruction - Σελίδα 231
των Warren Colburn - 1831 - 276 σελίδες
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## An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1838 - 276 σελίδες
...the terms are now equal, and one of them being multiplied by the whole number of terms will give the whole sum : thus Hence, the sum of a series of numbers in progression by differ- . .-» ence is one half of the product of the number of terms by the sum of the, first and...

## The Mercantile Arithmetic: Adapted to the Commerece of the United States, in ...

Michael Walsh - 1838 - 327 σελίδες
...two extremes by the whole number of terms, the product is the total of all the terms. EXAMPLES. 1 . How many strokes does the hammer of a clock strike in 12 hours ? 12 -f \ = 13 then 13X6 = 78. Ans. 2. A man buys 17 yards of cloth, and gave for the first yard 2s....

## Mental and Practical Arithmetic

Charles Davies - 1838 - 288 σελίδες
...terms. 100 last term 1 02 sum of extremes 11 half the number of terms 1122 sum of series. Ans. 1122. 2. How many strokes does the hammer of a clock strike in 12 hours ? Ans. 78. 3. The first- term of a series is 2, the common difference 4, and the number of terms 9,...

## A Practical and Theoretical System of Arithmetic: Containing a New System of ...

George Willson - 1838 - 192 σελίδες
...half the number of terms ; or, multiply by the whole number of terms, and take half the product. » 1. How many strokes does the hammer of a clock strike in 12 hours 1 Half number of terms =6. Extremes 1 + 12=13. 13X6=78. Ans. PROBLEM II. — The first term, the number...

## An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1839 - 276 σελίδες
...of them being multiplied by the whole number of terms will give the whole sum : thus .«-.'n(o"+*) 2 Hence, the sum of a series of numbers in, progression...does the hammer of a clock strike in 12 hours ? a = 1, I = 12, and n = 12. S = 12 (1 + 12) — m Ans ?8 strokes In the formula I — a + (n — 1)»";...

## An Algebra Upon the Inductive Method of Instruction

John Hopkins Harney - 1840 - 288 σελίδες
...number of terms, and divide by 2. 10. What is the sum of 20 terms of the series 1, 2, 3, 4, 5, &c. 11. How many strokes does the hammer of a clock strike in 12 hours? 12. What is the sum of 15 terms of a series, whose first term is 5, and common difference 2 ? 13. If...

## Arithmetic, Designed for Academies and Schools

Charles Davies - 1843 - 12 σελίδες
...number of terms. II half the number of terms 102 sum of extremes 1122 sum of series. Ans. 1122. 2. How many strokes does the hammer of a clock strike in 12 hours ? , Ans. 78. 3- The first term of a series is 2, the common difference 4, and the number of terms 9,...

## The practical arithmetic

...? Here (2 + 8) X 31 = 10 x 34 := 35. Ans. 2. What is the sum of 9i, 7£, 5J, and Ц ? .Ins. 26. 3. How many strokes does the hammer of a clock strike in 12 hours? •*»*• 78. 4. If lOOstonesbeplacedin a straight line, one yard asunder, and the first one yard...

## An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1844 - 276 σελίδες
...the terms are now equal, and one of them being multiplied by the whole number of terms will give the whole sum : thus Hence, the sum of a series of numbers...does the hammer of a clock strike in 12 hours ? a — 1, I= 12, and n = 12. 8 - 12 0 + 12) = 78. Ans. 78 strokes In the formula I ==. a + (n — 1) r...

## An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1844 - 276 σελίδες
...the terms are now equal, and one of them being multiplied by the whole number of terms will give the whole sum : thus Hence, the sum of a series of numbers...strokes does the hammer of a clock strike in 12 hours ? a=l, I = 12, and n = 12. S = 12 (* '+ 12) = 7.8. Ans. 78 strokes In the formula I = a -f- (n —...