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IQ Tests in Logical Thinking : Number Sequences I

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What number comes in the blank in each sequence below?

1. 4, 8, 16, 32, 64, _______
Answer: 128
Each number is multiplied by 2 to get the next number.


2. 2, 3, 5, 7, 11, 13, 17, 19, _______
Answer: 23
These are the prime numbers (i.e., numbers whose only factors are one and the number itself).


3. 1, 3, 6, 10, 15, _______
Answer: 21
3 - 1 = 2; 6 - 3 = 3; 10 - 6 = 4; 15 - 10 = 5;
The differences between two consecutive numbers are 2, 3, 4, 5, 6, ...
So, 21 - 15 = 6.
Alternatively, 1 + 2 = 3; 1 + 2 + 3 = 6; 1 + 2 + 3 + 4 = 10;
1 + 2 + 3 + 4 + 5 = 15; 1 + 2 + 3 + 4 + 5 + 6 = 21;
The nth term in the sequence is given by n (n + 1)/2. The numbers are often referred to as triangular numbers.



4. 500, 475, 425, 350, 250, _______
Answer: 125
500 - 475 = 25; 475 - 425 = 50; 425 - 350 = 75; 350 - 250 = 100;
The differences between two consecutive numbers are 25, 50, 75, 100, 125, ...
So, 250 - 125 = 125.


5. 200, 196, 180, 116, _______
Answer: -140
200 - 196 = 4; 196 - 180 = 16; 180 - 116 = 64;
The differences between two consecutive numbers are 4, 16, 64, ... (each number starting with 4 is multiplied by 4 to get the next number).
So, 116 - 4(64) = 116 - 256 = -140.


6. 987, 878, _______, 660, 551, 442
Answer: 769
987 - 109 = 878; 878 - 109 = 769; 769 - 109 = 660;
660 - 109 = 551; 551 - 109 = 442;
The difference between two consecutive numbers is 109.


7. 213, 426, _______, 852, 1065, 1278
Answer: 639
213 + 213 = 426; 426 + 213 = 639; 639 + 213 = 852;
852 + 213 = 1065; 1065 + 213 = 1278;
The numbers simply increase by 213.


8. 144, 121, 100, _______, 64, 49
Answer: 81
The terms are merely the squares of integers starting with 12 in descending order. Thus,
122 = 12 x 12 = 144; 112 = 11 x 11 = 121; 102 = 10 x 10 = 100;
92 = 9 x 9 = 81; 82 = 8 x 8 = 64; 72 = 7 x 7 = 49;
Alternatively, the differences between consecutive terms form the following simple sequence: 23, 21, 19, 17, 15.


9. 8, 27, 64, _______, 216, 343
Answer: 125
The terms are merely the cubes of integers starting with 2. Thus,
23 = 2 x 2 x 2 = 8; 33 = 3 x 3 x 3 = 27; 43 = 4 x 4 x 4 = 64;
53 = 5 x 5 x 5 = 125; 63 = 6 x 6 x 6 = 216; 73 = 7 x 7 x 7 = 343;


10. 2, 3, 4, 12, 6, 23, 8, 36, 10, _______
Answer: 51
The odd terms of the sequence are simply even numbers.
The even terms are 3, 12, 23, 36, ...
12 - 3 = 9; 23 - 12 = 11; 36 - 23 = 13;
The differences between two consecutive even terms are 9, 11, 13, 15, ...
So, 51 - 36 = 15.


11. 3, 10, 20, 27, _______, 44
Answer: 37
The odd terms continually increase by 17, i.e., 3, 20, 37, ...
The even terms also continually increase by 17, i.e., 10, 27, 44, ...
Alternatively, add 7 and 10 alternately starting with 3.


12. 2, 7, 11, 16, _______, 25
Answer: 20
The odd terms continually increase by 9, i.e., 2, 11, 20, ...
The even terms also continually increase by 9, i.e., 7, 16, 25, ...
Alternatively, add 5 and 4 alternately starting with 2.


13. _______, 0.99, 9.9, 99, 990, 9900
Answer: 0.099
Each number is one-tenth the number following it.
Thus, (1/10) x 0.99 = 0.099


14. 2.5, 3.75, _______, 8.4375, 12.65625
Answer: 5.625
Each number is 1.5 times the number preceding it.
Thus, 1.5 x 3.75 = 5.625


15. 243, 162, 108, 72, _______, 32
Answer: 48
Each number is two-thirds the number preceding it.
Thus, 72 x 2/3 = 48


16. 1/24, _______, 7/18, 10/15, 13/12, 16/9
Answer: 4/21
The numerators (starting with 1) increase continually by 3, and the denominators (starting with 24) decrease continually by 3.
The numerators are 1, 4, 7, 10, 13, 16, ...
The denominators are 24, 21, 18, 15, 12, 9, ...


17. 2, 6, 14, _______, 62, 126
Answer: 30
6 - 2 = 4; 14 - 6 = 8; 30 - 14 = 16; 62 - 30 = 32; 126 - 62 = 64
The differences between two consecutive numbers are 4, 8, 16, 32, 64, ... (a sequence where each number is multiplied by 2 to get the next number
starting with 4).


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