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A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 meter in the alternate minute. In which minute, he reaches the top?
How many figures (digits) are required to number a book containing 200 pages?
5. The positive sequence is defined by for n ≥ 2. If , then the n-th term in the sequence is
(a) 5n – 5
(b) 5n – 2
(d) 5n + 2
(e) 5n + 7
In the simple light show pictured above, a light starts at the center (white) at time zero and moves once every second in the following pattern: from white (W) to blue (B), back to white, then to green (G), back to white, then to red (R), and back to white—in a counter-clockwise direction. If the light continues to move in this way, what will be the color sequence from the 208th second to the 209th second?
(A) white to green
(B) white to blue
(C) white to red
(D) red to white
(E) green to white
7. In the sequence 12, 24, 72, 264…, where 12 is the first term, which of the following could denote the nth term?
8. In a sequence of number, the first term is 6. Each successive term following the first is calculated by adding 2 to the previous term and then dividing by -1. What is the value of the 101st term subtracted from the 70th term?
9. The first three terms of a geometric sequence are k, 6k and 36k. For how many values of k between 1 and 10 inclusive does the sequence contain only even integers?
The 5 numbers shown above are repeated indefinitely, in that order, to form a sequence. What is the product of the first 20 terms of the sequence?
11. Let an represent the nth term of a particular sequence. If a2 = 54 and each term except the first is equal to the previous term divided by 3, then what is the first term that is NOT an integer?
– 2, 4, -8. . .
12. In the sequence above, each term after the second can be found by multiplying the two preceding terms together. For example, the third term is – 2 *4 = -8. How many of the first 139 terms of this sequence are negative?
13. If A is the sum of the integers from 1 to 50 and B is the sum of the integers from 51 to 100, what is the value of B – A?
14. Consider the sequence 2, 6, 18, 54, 162, … in which each term after the first term is 3 times the preceding term. If the 48th term is a and the 51st term is b, what is the value of b/a ?
The number of cells growing in a particular Petri dish doubles every 30 minutes. If at 8:00 A M. there were 60 cells in the dish, how many were there at noon of the same day?
(A) 60 *2–8
(B) 60 *2–4
(C) 60 *24
(D) 60 *44
(E) 60 *48
Jessica created a sequence of five numbers. She chose a number for the first term and got each successive term by using the following rule: alternately add 6 to the preceding term and double the preceding term. The second term of Jessica’s sequence was 6 more than the first, the third term was double the second, the fourth term was 6 more than the third, and the fifth term was double the fourth. If the fifth number was 1996, what number did Jessica choose for the first term?
17. Consider the sequence 1, 2, 3, 1, 2, 3, 1, 2, 3, … What is the sum of the first 100 terms?
18. A population that starts at 100 and doubles after eight years can be expressed as the following where t stands for the number of years that have elapsed from the start:
(C) 100x2t - 8
19. The sum of all numbers of the form 2K + 1, where K takes on integral values from 1 to n, is
(B) n(n + 1)
(C) n(n + 2)
(D) (n + 1)2
(E) (n + 1)(n + 2)
20. If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =
D. 220 - 1
E. 221 - 1
21. The sequence a1, a2, … , an, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x?
22. Express the infinite decimal 0.212121... as a common fraction.
23. The sum of all numbers of the form 2K + 1, where K takes on integral values from 1 to n2, is
(B) n2(n2 + 1)
(C) n2(n2 + 2)
(D) (n + 1)4
(E) (n4 + 1)(n2 + 2)
29. What is the ratio of an to an-1 if an = 7n n!
a) 7n b) 7n+1 c) 7n d) 7n e) 7n/n
30. If a15 = 19 and a17 = 5 for an arithmetic sequence then what is a11.
a) 12 b) 25 c) 26 d) 34 e) 47
31. If 2n + 1, 3n – 4 and 2n – 3 form an arithmetic sequence then what is n ?
a) 6 b) 5 c) 4 d) 3 e) 2
32. Find the units digits of the number
33. Find the remainder when is divided by 12.
35. Find the sum of integers satisfying , and the remainder of which is 1 when divided by 3?
36. If a1=3, d=4 and (an) is arithmetic sequence then what is which term will be 91?
a) 18 b) 20 c) 23 d) 25 e) 30
37. In the figure a square is drawn connecting the middle points of each side of a square with a side length 6 and this procedure is repeated. What is the perimeter of the 9th square that is drawn?
A) B) C) 3 D) E)
38. Which one is not a subsequence of ?
A) B) C) D) E)
1. A man earns $20 on the first day and spends $15 on the next day. He again earns $20 on the third day and spends $15 on the fourth day. If he continues to save like this, how soon will he have $60 in hand?
(a) On 17th day
(b) On 27th day
(c) On 30th day
(d) On 40th day
(e) On 45th day
2. In a geometric sequence, each term is a constant multiple of the preceding one. If the first three terms in a geometric sequence are - 2, x, and - 8, which of the following could be the sixth term in the sequence?
3. In a geometric series, each term is a constant multiple of the preceding one. If x and y are the first two terms in a geometric series, which of the following represents the third term in the series?
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