2,16,12,3,28,23,1,36,19,5,8,21 reasoning question
Answers
solve by these steps
Step-by-step explanation:
1. Series with a constant difference
In this kind of series, any 2 consecutive numbers have the same difference between them.
For example : 1 , 5 , 9 , 13 , ?
We can observe that we are adding 4 to the previous number to obtain the next number. So, answer here will be 13+4 = 17.
2. Series with an increasing difference
In this type of series, the difference between two consecutive terms keep on increasing as we move forward in a series. Let us try to use this theory in a question.
1,2,4,7,11,16,?
We can clearly observe that the series is increasing with the difference : +1, +2, +3 ,+4 , +5.
So, we will obtain our number by adding 6 to 16 which gives us 22.
3. Series with a decreasing difference
In this type of series, the difference between two consecutive terms keep on decreasing as we move forward in a series. Let us try to use this with some modification in the previous question that we did.
16,11,7,4,2, ?
We can clearly observe that the series is decreasing with the difference : -5, -4, -3 ,-2 .
So, we will obtain our number by subtracting 1 from 2 which gives us 1.
4. Squares/ Cubes series
We can have series where the terms are related to the squares/ cubes of numbers. We can have a lot of variations here. Let us look at some of the possibilities.
1, 9, 25, 49 , ?
We can observe that the above series is square of odd numbers starting from one. So our answer will be 9^2 = 81.
Let us look at another example:
1 , 1 , 2 , 4 , 3 , 9 , 4 , ?
We observe here that the series is formed by writing numbers starting from 1 along with its square as the next number i.e. ( 1 , 12) , (2, 22) and so on. So we obtain our answer as 16 which is 42.
Consider the following question:
9 , 28 , ? , 126.
The answer for above question will be 65, let us discuss how.
9 , 28 , ? , 126.
( 23+1) (33+1) (53+1)
The blank should have 43+1. Hence, the answer is 65.
5. Combination of different operations
This kind of series has more than 1 type of arithmetic operations which have been performed or it can also have 2 different series which have been combined to form a single series. This kind of series is the the most asked and the most important among all the types of series that we have discussed so far.
Consider the series:
1, 3 , 6 , 2 , 6 , 9 , 3 , 9 , ?
The first term 1 is multiplied by 3 to give the second term, 3 has been added to the second term to get the third term. The next term is 2 which is 1 more than the 1st term. It is multiplied with 3 to give next term and the process is continued. With this process, we obtain our answer as 12.
Consider the series:
6, 10 , 7, 11 , 8 , 12 , ?
We can see that the above series is a combination of 2 simple series:
1st , 3rd , 5th terms make an increasing series of 6 , 7 , 8….. . The 2nd , 4th and 7th term make a series of 10 , 11 , 12… . So, our answer will be 9 which is the 7th term of the original series.
6. Miscellaneous series
Some series do not come under any of the above mentioned categories but are very important and also asked in many examinations.
The series of prime numbers or any other related operation done on it comes under this category.
Consider the example:
9, 25 , 49 , 121 , ?
The above series is the squares of prime numbers. So next term will be square of 13 which is 169.
Try out the following questions:
1. 49 , 1625 , 3649 , ?
Solution : Each term in the above series is combination of squares of 2 numbers i.e.
22 32 , 42 52 , 62 72 . So, our answer will be 6481.
2. Look at this series: 40, 40, 26, 26 , 12 , ? … What number should come next?
Solution:Answer is 12. Each number is repeated or firstly 0 is added to each number and then 14 is subtracted from it.
3. 2 , 4 , 11 , 37 , ?
Solution: (2*1) + 2 =4
(4*2) + 3 = 11
(11*3) + 4 =37
(37*4) + 5 = 153
4. 6 , 3 , 3, 4.5 , 9, ?
Solution : We see that no decreasing or increasing difference logic is applicable here. So, we find out the ratios of every term with its predecessor. We get the following values: 0.5 , 1 , 1.5 , 2 . This makes it clear that 9 should be multiplied by 2.5 in order to obtain the next number.
Therefore, the answer is 9* 2.5 = 22.5 .
5. 8 , 15 , 26 , 39 , ?
Solution: Let us start by finding out the difference between every pair of consecutive terms:
15-8=7
26-15=11
39-26=13
We observe that the difference is the series of prime numbers. According to this logic , 17 should be added to 39 to obtain the answer. Hence, the answer is 56.
6. Consider the series: 42, 40, 36, 34, 30, 28, … What number should come next?
Solution: 24 is the answer . we are performing the operations : – 2, -4. )
7. 24 , 30 , 36 , 42 , 54 , 60 , 68 . Find out the wrong term in the series.
Solution: Each term is the sum of 2 consecutive prime numbers.
24 = 11+ 13
30 = 13+ 17
36= 17+ 19
So, according to this logic, 54 is the wrong term. We should have 52 in its place.
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