A Review of Algebra

by Romeyn Henry Rivenburg

GEOMETRICAL PROGRESSION

1. Define a geometrical progression.

Learn to derive the four formulas in geometrical progression:

2. How many terms must be taken from the series 9, 18, 36, ··· to make a total of 567?

3. In the G. P. 2, 6, 18, ···, which term is 486?

4. Find x, if

are in geometrical progression.

5. How can you turn a G. P. into an equation?

6. Insert 4 geometrical means between 4 and 972.

7. Insert 6 geometrical means between

and 5120.

8. Given

find r and S.

9. If the first term of a geometrical progression is 12 and the sum to infinity is 36, find the 4th term.

10. If the series

··· be an A. P., find the 97th term. If a G. P., find the sum to infinity.

11. The third term of a geometrical progression is 36; the 6th term is 972. Find the first and second terms.

12. Insert between 6 and 16 two numbers, such that the first three of the four shall be in arithmetical progression, and the last three in geometrical progression.

13. A rubber ball falls from a height of 40 inches and on each rebound rises 40% of the previous height. Find by formula how far it falls on its eighth descent. (Yale.)

Reference: The chapter on Geometrical Progression in any algebra.

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