Math Olympiad 5

Pattern Problem( Week 33 Evaluation)

1. What is the next term of the following sequence? 2, 6, 18, 54, 162,

2. How many two-digit numbers are there in which the tens digit is greater than the ones digit?

3. Lisa is making a necklace by stringing beads of different colors. She strings beads in the order of red, orange, yellow, green, blue, and white. If her necklace design begins with a red bead and ends with a yellow bead, what is the possible number of beads that her necklace could contain?

A) 20

B) 40

C) 25

D) 21

4. 9ⁿ is n 9s multiplied together. What is the end digit of 9¹⁵⁸?

5. Below is a repeating decimal that the set of digits 90123 repeat after the decimal point endlessly.
0.90123 = 0.901239012390123...
Which digit will fall in the 982nd place to the right of the decimal point?

6. During the holiday shopping season, Jennifer worked at a gift store as a part-time job. The boss of the store set the first day salary and then increased $2 each day after the first day. She earned a total of $224 in 7 days. How much (in dollars) did she earn on the first day?

7. The following sequence of numbers are placed in the table as shown. Note that each number in the sequence is an odd number. If the pattern continues, in which column will the number 231 appear?

I	II	III	IV	V	VI	VII	VIII	IX	X
	1	3	5	7	9	11	13	15	17
19	21	23	25	27	29	31	33	35	37
39	41	43	45	47	49	51	53	55	57
59	...	...	...	...	...	...	...	...	...

8. When expressing

as a decimal, you get 0.0909090909090909..., what is the 30th place to the right of the decimal point?

9. The following sequence of numbers are placed in the table as shown. Note that each number in the sequence is a multiple of 8 plus 1, and 1 is in the first row. If the pattern continues, what number will appear in the cell corresponding to the 16th row and column I?

I	II	III	IV	V	VI	VII	VIII
						1	9
17	25	33	41	49	57	65	73
81	89	97	105	113	121	129	137
145	...	...	...	...	...	...	...

10. Single-color beads of red, orange, yellow, green, black, blue, or white are placed in a line so that the pattern of red, orange, yellow, green, black, blue, white, red, orange, yellow, green, black, blue, white,... repeats throughout. If the first bead in the line is red,which of the following bead is orange?