18. A young man receiving a legacy of $48000 invested one half in 5% railway bonds at 957, and the other half in 6% stock at 1197; what income did he secure? 19. A owns a farm which rents for $320.40 per yr. If he should sell the farm for $8010 and invest the proceeds in U.S. 4's at 111, will his yearly income be increased or diminished, and how much? 20. A capitalist drew the quarterly interest on his U.S. 4's, amounting to $540, and afterwards sold the bonds at $1245; what were the proceeds of the sale? 21. A lady invested $20948.75 as follows: $6160 in Maryland 6's at 961, $8225 in manufacturing stock at 87 paying 8% annual dividends, and the remainder in steamboat stock at 735 paying 10% annual dividends; what was her total income? English government bonds are called Consols. 22. A man had £2400 in the 23% consols; he sold out at 991 and invested the proceeds in 4% railway bonds, thereby increasing his income by £6 a yr; at what price did he buy the bonds? 23. A man having an income of £352 a yr. in the 23% consols, sells out at 97 and invests the proceeds in 4% railway bonds, thereby increasing his income £48 a yr; at what price were the bonds purchased? CHAPTER XIV. PROGRESSIONS. 275. A series of numbers which increases or decreases regularly is called a Progression. For instance, are progressions. 3, 5, 7, 9, 11, or 23, 20, 17, 14, 11, 8, or 3, 6, 12, 24, or 81, 27, 9, 3, 1, §, †, It will be noticed that in the first two progressions the series are made by successive additions or subtractions, while in the last two the series are made by successive multiplications or divisions. The first are called Arithmetical Progressions (increasing or decreasing). The second are called Geometrical Progressions (increasing or decreasing). 277. Any three of these five being given, the other two may be found. In the arithmetical progression, 7, 10, 13, 16, 19, 22, 25, it is evident that the last term is a plus six d, or that the first term is 7 minus six d. It is also evident that if a and I be added and the sum÷2, the result will be the middle term; and that if each term be changed so as to contain as many units as the middle term the sum of the new series will be the same as the sum of the original series. By these formulas all examples in arithmetical progression may be solved. 7. Insert 3 means between 2 and 12. 8. Find the series of 8 terms when the 3d term is 14 and the 7th term is 26. 9. Find the series of 9 terms when a 10.8 and the 6th term = 4.8. (The ratio is the relation existing between any two successive terms. It is the constant multiplier by which any term is found from the preceding term.) Any three of these five being given, the other two may be found. |