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HARMONICAL PROGRESSION. 313 Find the series in which

14. The 10th term is 320 and the 6th term 20. 15. The 5th term is 27 16 and the 9th term is 13. 16. The 7th term is 625 and the 4th term -5. 17. The 3d term is 9 16 and the 6th term -4 12. 18. Divide 183 into three parts in G. P. such that the sum of the first and third is 2 1 20 times the second. 19. Show that the product of any odd number of consecutive terms of a G. P. will be equal to the nth power of the middle term, n being the number of terms. 20. The first two terms of an infinite G. P. are together equal to 1, and every term is twice the sum of all the terms which follow. Find the series.

Sum the following series: 21. y2 + 2b, y4 + 4b, y6 + 6b, ... to n terms. 22. ?jtlV?, 1, ^-^^^ ...to infinity. 3-2V2 3 + 2V2 23. Vi W'^^ fVf, to infinity. 24. 2 n — 1, 4 n + i, 6 w — j, ... to 2 n terms. 25. The sum of four numbers in G. P. is equal to the common ratio plus 1, and the first term is 1 17. Find the numbers. 26. The difference between the first and second of four numbers in G. P. is 96, and the difference between the third and fourth is 6. Find the numbers. 27. The sum of $225 was divided among four persons in such a manner that the shares were in G. P., and the difference between the greatest and least was to the difference between the means as 21 to 6, Find the share of each. 28. The sum of three numbers in G. P. is 13, and the sum of their reciprocals is 13 9. Find the numbers.

HARMONICAL PROGRESSION.

383. Definition. Three quantities, a, b, c, are said to be in Harmonical Progression when q c = a - b b — c

Any number of quantities are said to be in Harmonical Progression when every three consecutive terms are in Harmonical Progression.