10. Find the fourth and sixth terms of the geometric progression with first term 2 and ratio -3.

11. Find the next three terms of the geometric progression 2, 14, 98, ... .

12. Find the next three terms of the geometric progression 6, -2, 2/3, -2/9, ... .

13. Find both possible values of x if 7, x, 252 are three consecutive terms of a geometric progression.

14. Find all possible values of y if 400, y, 16 are three consecutive terms of a geometric progression.

15. Find a compact expression for each of the following:

(a) 1 + 7 + 7² + 7³ + ... + 7⁹⁹⁹.

(b) 1 - 7 + 7² - 7³ + ... - 7⁹⁹⁹.

(c) 1 + 7 + 7² + 7³ + ... + 7^n-1.

16. Find a compact expression for each of the following:

17. Find n, given that 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 =

^*18. Find m, given that 1 + 2 + 3 + 4 + ... + 1000 =

19. Given that a is the average of the numbers r and s, show that r, a, s are three consecutive terms of an arithmetic progression and that their sum is 3a.

20. Show that r³, r²s, rs², s³ are four consecutive terms of a geometric progression and that their sum is (r⁴ - s⁴)/(r - s).

Sunday, March 15, 1998