Page:Elementary algebra (1896).djvu/329

GEOMETRICAL PROGRESSION. 311 4. Find the 8th and 12th terms of the series 81, -27, 9,. 5. Find the 14th and 7th terms of the series 1 64, 1 32, 1 16. 6. Find the 4th and 8th terms of the series .008, .04, .2, ....

Find the last term in the following series:

7. 2, 4, 8, ... to 9 terms. 8. 2, -6, 18, ... to 8 terms. 9. 2, 3, 41, ... to 6 terms. x 10. 3, -3 2, 3 3, ... to 2n terms. 11. x, x3, x5, to p terms. 12. x, 1, 1 x to 30 terms. 13. Insert 3 geometric means between 486 and 6. 14. Insert 4 geometric means between i and 128. 15. Insert 6 geometric means between 56 and — 7 16. 16. Insert 5 geometric means between 32 81 and 4 1 2.

Find the last term and the sum of the following series:

17. 3, 6, 12, ... to 8 terms. 18. 6, -18, 54, ... to 6 terms. 19. 64, 32, 16, ... to 10 terms. 20. 8.1, 2.7, .9, ... to 7 terms. 21. to 8 terms. 22. 4 1 2, 1 12, 1 2 to 9 terms.

Find the sum of the series :

23. 3, - 1, 1,... to 6 terms. 24. 1 2, 1 3, 2 9, ... to 7 terms. 25. -2 5, 1 2, -5 8, ••• to 6 terms. 26. 1, -1 2, 1 4, ... to 12 terms. 27. 9, - 6, 4, ... to 7 terms. 28. 23, -1 6, 1 24 ... to 8 terms. 30. 2, -4, 8, ... to 2 p terms. 29. 1, 3, 32, ... to p terms. 31. 1 3, 1, 3 3 ... to 8 terms. 32. a, a3, a5 to a terms. 33. 1 2, -2, 2 2 ... to 7 terms. 34. 2, 6, 3 2, to 12 terms.

380. Infinite Geometrical Series. Consider the series

The sum. to m terms =

From this result it appears that however many terms be taken the sum of the above series is always less than 2. Also we see that, by making n sufficiently large, we can