Problems for Chapter 4

1. (a) Find the second, third, and fourth terms of the arithmetic progression with the first term -11 and difference 7.

(b) Find the next three terms of the arithmetic progression -3, -7, -11, -15, ... .

2. (a) Find the second, third, and fourth terms of the arithmetic progression with the first term 8 and difference -3.

(b) Find the next three terms of the arithmetic progression 7/4, 1, 1/4, -1/2, -5/4, -2, ... .

3. Find the 90th term of each of the following arithmetic progressions:

(a) 11, 22, 33, 44, ... .

(b) 14, 25, 36, 47, ... .

(c) 9, 20, 31, 42, ... .

4. For each of the following geometric progressions, find e so that 3^e is the 80th term.

(a) 3, 9, 27, ... .

(b) 1, 3, 9, ... .

(c) 81, 243, 729, ... .

5. Find x, given that 15, x, 18 are consecutive terms of an arithmetic progression.

6. Find x and y so that 14, x, y, 9 are consecutive terms of an arithmetic progression.

7. Sum the following:

(a) 7/3 + 2/3 + (-1) + (-8/3) + (-13/3) + ... + (-1003/3).

(b) (-6) + (-2) + 2 + 6 + 10 + ... + 2002.

(c) The first ninety terms of 7/4, 1, 1/4, -1/2, -5/4, -2, ... .

(d) The first n odd positive integers, that is, 1 + 3 + 5 + ... + (2n - 1).

8. Sum the following:

(a) 12 + 5 + (-2) + (-9) + ... + (-1073).

(b) (-9/5) + (-1) + (-1/5) + 3/5 + 7/5 + 11/5 + ... + 2407.

(c) The first eighty terms of -3, -7, -11, -15, ... .

(d) The first n terms of the arithmetic progression a, a + d, a + 2d, ... .

9. Find the fourth, seventh, and ninth terms of the geometric progression with first term 2 and ratio 3.
 

 
 Sunday, March 15, 1998