 | Warren Colburn - 1838 - 282 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... | |
 | Michael Walsh - 1838 - 346 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.... | |
 | Charles Davies - 1838 - 292 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,... | |
 | George Willson - 1838 - 194 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... | |
 | Warren Colburn - 1839 - 308 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)»";... | |
 | John H. Harney - 1840 - 298 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... | |
 | Charles DAVIES (LL.D.) - 1843 - 348 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,... | |
 | John Darby (teacher of mathematics.) - 1843 - 236 σελίδες
...? 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... | |
 | Warren Colburn - 1844 - 280 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... | |
 | Warren Colburn - 1844 - 280 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 —... | |
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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. 
