Part: 3 Number Sequence Solved Examples ~ Explore Your Knowledge

Sunday, March 11, 2012

Part: 3 Number Sequence Solved Examples

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1. What is the next digit of the series 1,2,3,4,5,7,....?
A) 9 B) 14      C) 11      D) 16      E) 18

Solve: Numbers: 1     2     3     5     7     11
Differences: 1 1    2    2    4
Ans: (C)

2. Which of the next number in the series 2,5,7,8,8,....?
A) 6      B) 7      C) 10      D) 11      E ) None of these

Solve: Numbers: 2      5      7      8      8      7
Differences:        3      2      1       0      -1
Ans: (B)

3. What is the next number in the series: 1,4,9,16,......?
A) 20      B) 21      C) 22      D) 23      E) 25

Solve: 1² =1
   2² =4
    3² =9
4² = 16
         :. 5²=25
Ans: (E)

4. The first 5 numbers in a regular sequence are 4,10, 22, 46 & 94 . What is the next number in the sequence?
A) 142      B) 154       C) 176      D) 182      E) 190
Sol. Numbers: 4      10      22      46      94       190
Differences:       6    12    24    48 96
Ans: (E)

5. Find the next two numbers.
(i) 112,96,80,72,64,60,56,54,---,---.
Sol: Numbers: 112    96    80    72    64    60    56    54    52    51
    Differences:        16      16      8         8        4       4         2         2        1
Ans: 52 & 51

(ii) 3,9,5,11,7,---,---.
Sol:       3    9    5    11    7    13    9
Sequence: 3, 5, 7, 9
   9, 11, 11
Ans. 13 & 9

(iii) 1, 2, 3, 5, 7,--,--.
Sol: Numbers: 1      2      3      5      7    11 15
     Difference:    1 1    2    2    4 4
Ans: 11& 15

(iv) 2,9,6,7,18,5,--,--.
Sol: Here, we have two sequences.
2 6 18 54
=2x3    =2x9 =2x27
9      7         5      3
   2    2 2
:. The sequence is 2,9,7,18,5,54,3.
Ans: 54 & 3

(v) 8,14,24,42,--,--.
Sol: Numbers: 8      14      24      42
   Differences:       6         10     18
We are not getting any sequence. Again taking difference we get
8      14      24      42    [42+34=76]       [76+66=142]
    6         10     18     [18+16=34]         [34+32=142]
   4    8 16 32
:. The sequence is 8,14,24,42,76,142..
Ans: 76 m& 142

6. 1+ 2+ 3+.......................+100 = ?
Sol: We know, sum = n(n+1)/2 = 100(100+1)/2 = (100x101)/2 = 5050
Ans: 5050

7. The next number in the geometric progression 5, 10, 20 is:
Sol: Please observe that
1ts number    5x1 = 5
2th number     5x2 = 10
3th number 5x2x2 = 20
Following this same pattern, we get the next number as 5x2x2x2 = 40
Ans: (D)

8. What is the next number in the series: 1,2,3,6,11,20,37,--.?
Sol: These types of problems don't have any fixed solution technique. You will have to look for patterns in the numbers. In this series, if we take a closer look, we see that
6   = 1+2+3
11 = 2+3+6
20 = 3+6+11
37 = 6+11+20
So, the next number should be (11+20+37) = 68
Ans: 68

9. What is the sum of the integers in the table below:
A) 28      B) 112      C) 336      D) 448      E) 789

Sol: simply trying to add up all the numbers will be too cumbersome. So, we apply a technique. Please note that.
2th row = -2x1th row
3th row = 3x 1th row
& so on.
So, we can write that the sum of all the number is
1th row x (1-2+3-4+5_6+7)
(1+2+3+.........................+7)x4 = ((7x8)/2)x4
= 112
Ans: (B)