TOTAL MARK / 30 |
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Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. If the first term of a sequence is 3 and the common difference is 4, what is the 23rd term in the sequence?
a. | 88 | c. | 95 |
b. | 87 | d. | 91 |
____ 2. What is the general term of the sequence: 6, 42, 294, 2058,14406, …
____ 3. If the 9th term in a geometric sequence is 45 927 and the common ratio is 3, then what is the first term?
a. | 7 | c. | 6 |
b. | 8 | d. | 9 |
____ 4. Find the next three terms of the sequence: 4, 11, 30, 67, …
a. | 125, 216, 343 | c. | 128, 219, 346 |
b. | 84, 246, 732 | d. | 246, 732, 2190 |
____ 5. Determine whether the sequence is geometric, arithmetic, neither with a defined general term, or neither with an undefined term.
8, 42, 76, 110, …
a. | Arithmetic | c. | Neither – Definable |
b. | Geometric | d. | Neither – Undefinable |
____ 6. Determine the sum of the arithmetic sequence: 5 + 18+ 31 + 44 + … +. 161.
a. | 1079 | c. | 996 |
b. | 1992 | d. | 2158 |
____ 7. Determine the sum of the geometric series 3 + 15 + 75 + 375 + … + 46 875.
a. | 58 593 | c. | 19 531 |
b. | 11 718 | d. | 292 968 |
____ 8. Expand the binomial (2x + 1)4
PART II Short Answer:
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9. Find the general term of the sequence 1, 1000, 10 000 000, 1 000 000 000 000 000, …
10. You are given a sequence: 1, 8, 4, 11, 7, 14, 10, 17, …
Describe in words how the sequence is obtained.
11. Calculate the sum of the series: –396 – 308 – 220 – 132 – … + 836.
12. Calculate the sum of the Geometric series
13. Expand and simplify the binomial power using Pascal’s Triangle
Problem
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14. The triangular numbers are the numbers in the sequence: 1, 3, 6, 10, 15, …
a) Determine the next three triangular numbers
b) Find the recursive formula for the sequence
c) Find the General form for the sequence