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1. |
Write an arithmetic sequence that has three arithmetic means between 3.5 and 2.7. |
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A. |
3.5, 3.25, 3.05, 2.85, 2.7 |
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B. |
3.5, 3.3, 3.1, 2.9, 2.7 |
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C. |
3.5, 3.35, 3.15, 2.95, 2.7 |
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D. |
3.5, 3.4, 3.1, 2.8, 2.7 |
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Hint |
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2. |
Write a sequence that has two geometric means between 7 and 448. |
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A. |
7, 29, 113, 448 |
B. |
7, 26, 110, 448 |
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C. |
7, 30, 144, 448 |
D. |
7, 28, 112, 448 |
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Hint |
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3. |
Find the fifth term of a geometric sequence whose first term is 6 and whose common ratio is  . |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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4. |
Find  . |
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A. |
7 |
B. |
does not exist |
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C. |
5 |
D. |
0 |
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Hint |
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5. |
Which series is a convergent geometric series? |
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A. |
 |
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B. |
 |
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C. |
 |
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D. |
 |
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Hint |
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6. |
Bob has a savings account that has an annual yield of 5%. Find the balance of the account after each of the first two years if his initial balance is $4000. |
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A. |
$4200, $4410 |
B. |
$4000, $4200 |
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C. |
$4200, $4400 |
D. |
$4200, $4500 |
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Hint |
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7. |
Find the first two iterates of the function f(z) = z + 3, if the initial value is 1 + i. |
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A. |
4i, 7i |
B. |
7 + i, 10 + i |
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C. |
4 + i, 7 + i |
D. |
4 + i, 10 + i |
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Hint |
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8. |
Which statement is not true? |
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A. |
6n - 1 is divisible by 5 for all positive integral values of n. |
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B. |
7n - 2n is divisible by 5 for all positive integral values of n. |
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C. |
7n + 2n is divisible by 9 for all positive integral values of n. |
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D. |
5n - 1 is divisible by 4 for all positive integral values of n. |
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Hint |
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9. |
In a certain arithmetic sequence, a1 = -38, d = 7, and ak = 74. Find k. |
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A. |
The sequence will never take on the value 74. |
B. |
6 |
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C. |
16 |
D. |
17 |
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Hint |
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10. |
Find the sum of the series -20 + 10 - 5 + … |
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A. |
The sum does not exist. |
B. |
-40 |
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C. |
-15 |
D. |
 |
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Hint |
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11. |
Write the general term of the series  |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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12. |
Find the sum  . |
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A. |
0 |
B. |
12 |
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C. |
8 |
D. |
The sum does not exist. |
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Hint |
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13. |
Write the series  in sigma notation. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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14. |
Rachel shoots seven free throws. Each free throw either goes in or does not. Find the number of possible combinations of free throws such that at least four go in. |
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A. |
64 |
B. |
21 |
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C. |
163 |
D. |
35 |
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Hint |
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15. |
Find the third term of the expansion of (6s + 2t)4. |
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A. |
144s2st2 |
B. |
6s2t2 |
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C. |
72s2t2 |
D. |
864s2t2 |
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Hint |
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16. |
Use the first four terms of the exponential series and a calculator to approximate the value of e0.28 to three decimal places. |
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A. |
0.33 |
B. |
0.76 |
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C. |
1.38 |
D. |
1.33 |
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Hint |
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17. |
Use the first three terms of the trigonometric series and a calculator to approximate the value of  to four decimal places. |
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A. |
0.6757 |
B. |
1.3243 |
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C. |
0.7074 |
D. |
0.7071 |
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Hint |
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18. |
If  , which statement verifies that Sn is valid for n = k + 1? |
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A. |
 |
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B. |
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C. |
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D. |
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Hint |
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