 | Elias Loomis - 1868 - 386 σελίδες
...that their sum shall be 210, and the last shall exceed the first by 90. Ans. 30, 60, and 120. Prob. 4. Find three numbers in geometrical progression such that their sum shall be 42, and the sum of the first and last shall be 34. Ans. 2, 8, and 32. Prob. 5. Find three numbers in... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 σελίδες
...0 to 4. Prove that if four quantities are in proportion, they are in proportion by composition. 8. Find three numbers in geometrical progression such that their sum shall be 42, and the sum of the first and the last shall be 34. 9. Expand (x + yf and (5a* — 4r*yf by the... | |
 | Horatio Nelson Robinson - 1872 - 436 σελίδες
...Ans. 4, 24, 144, and 864. 7. It is required to find three numbers in geometrical progression, euch that their sum shall be 14, and the sum of their squares 84. Ans. 2, 4, and 8. 8. There are four numbers in geometrical progression, the second of which is less... | |
 | Elias Loomis - 1873 - 396 σελίδες
...equation. Several of the following problems also have two solutions, if we admit negative values. Prob. 3. Find three numbers in geometrical progression such that their sum shall be 210, and the last shall exceed the first by 90. . An*. 30, 60, and 120. Prob. 4. Find three numbers... | |
 | Horatio Nelson Robinson - 1874 - 340 σελίδες
...and the sum of the squares of the first and last is 626 ; what are the numbers ? Ans. l, 5, 25. 12. It is required to find three numbers in geometrical...sum shall be 14, and the sum of their squares 84. Ans. 2, 4, and 8. 13. Of four numbers in geometrical progression, the second number is less than the... | |
 | James Bates Thomson - 1878 - 322 σελίδες
...last term ? 6. What is the i6th term of a series, the first term of which is 3, and the ratio 3 ? 7. Find three numbers in geometrical progression, such that their sum shall be 2 1, and the sum of their squares 189. Let the three numbers be x, <\/xy, and y. By the conditions,... | |
 | Webster Wells - 1879 - 468 σελίδες
...equations by the first, r* = — 8 ; whence, r — — 2. 48 48 Then, a = — == — — ¿, Ans. r 16 2. Find three numbers in geometrical progression, such...sum shall be 14, and the sum of their squares 84. Let a, ar, and a r2 denote the numbers. Then, by the conditions, a + ar + a r2 = 14 (1) 84 (2) Dividing... | |
 | Shelton Palmer Sanford - 1879 - 348 σελίδες
...unknown quantities in accordance with the principles of progression explained in the preceding pages. 1. Find three numbers in geometrical progression such that their sum shall be 13 and the sum of their squares 9L Analysis. Let a; = the first term and ^ = the ratio. The series... | |
 | Simon Newcomb - 1884 - 576 σελίδες
...m, m', n and n' fulfil the conditions m' = 2 (m — n) +1; '¿u' = m + n IQ. Find 7 terms of an AP such that their sum shall be 14 and the sum of their squares 84. 11. In an AP the product of the first and eighth terms is less by k than the product of the second... | |
 | 1885 - 286 σελίδες
...geometrical progression is 216, and the sum of the squares of the extremes is 328 ; what are the numbers? 86. It is required to find three numbers in geometrical...sum shall be 14, and the sum of their squares 84. 87. Three numbers are in arithmetical progression ; their sum is 27, and the product of the extremes... | |
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It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84. 
