number series 1
NUMBER SERIES
A number series can be considered as a collection of numbers in which all the terms are formed according to some particular rule or all the terms follow a particular pattern. The relation of any term to its proceeding term will be same throughout the series.
- The relation of any term to its proceeding term will be same throughout the series.
- We have to find out the rule in which the terms of the series are selected.
- We have to find out the missing number depending on that rule.
Some types of series
1. Prime Series : In which the terms are the prime numbers in order.
Examples:
(i): 2, 3, 5, 7, 11, 13, .
Here the terms of the series are the prime numbers in order. The Prime number after 13 is 17. So, the answer is 17.
(ii): 2, 5, 11,17,23, .
This series is by taking the alternative Prime numbers, after 23 the prime numbers are 29 and 31. So, the answer is 31
2. Addition Series : Each number in the series obtained by adding a specific number or series of numbers to previous number.
Examples:
i) 7, 10, 13, 16, 19, 22,
Each number is added by 3 to its previous number
So, the answer is 22 + 3 = 25.
ii) 10, 14, 19, 25, 32,
So, the answer is 32 + 8 = 40
iii) 5, 7, 10, 15, 22,
Each number in the series obtained by adding consecutive primes. So, the answer is 22 + 11 = 33.
3. Fibonacci Series : Every third number can be the sum of the preceding two numbers.
Examples:
i) 3, 5, 8, 13, 21,
Here starting from third number,
3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21, So, the answer is 13 + 21 = 34
ii) 6, 10, 16, 26, 42,
Here starting from third number,
6 + 10 = 16, 10 + 16 = 26, 16 + 26 = 42, So, the answer is
26 + 42 = 68
4. Difference Series : In which next term is obtained by substracting a fixed number from the previous term.
Example:
i) 87,76,65,54,43,32,?
Here, every number is 11 less than the previous number
so the answer is 32-11=21.
5. Multiple Series : In which next term is obtained by multiplying a number with the previous term.
Example:
i)3,6,12,24,48,96,?
Here, every number is double the previous number
so the answer is 96x2=192
6. n² Series :The series formed by Square numbers.
Examples:
i)1,9,25,49,81,?
The given series consists of squares of consecutive odd numbers
So the next term is 11²= 121.
ii)196,169,144,121,101 find the wrong one.
The series is 14²,13²,12²,11²,10²
but 10²=100 so, 101 is wrong.
7. n²+1 Series : Each term is a sum of a square and 1.
Example:
i) 5,17,37,65,?
This series pattern
2²+1=5,4²+1=17,6²+1=37,8²+1=65
so the answer is 10²+1=101
8. n²-1 Series : Each term is obtained by substracting a from a square number.
Example:
i)0,3,8,15,24,?
Series pattern
1n²-1=0,2n²-1=3,3n²-1=8,.....
So the answer is 6n²-1=35.
9. n²+n Series : Each term in the series is a sum of a number and its square.
Example:
i)6,12,20,30,42,56,?
Series pattern
2²+2,3²+3,4²+4,5²+5,6²+6,7²+7
The answer is 8²+8=72
10. n²-n Series : In which the terms are obtained by sustracting a number from square of that number.
Example:
i) 0,6,12,20,30,42,?
Series pattern
2²-2,3²-3,4²-4,5²-5,6²-6,7²-1
So the answer is 8²-8=56
11. n³ Series : The series formed by Cube numbers.
Example:
i) 64,125,216,343,?
Series pattern
4³,5³,6³,7³
The answer is 8³= 512.
12. n³+1 Series : Each term is a sum of a cube of a number and 1.
Example:
i) 9,28,65,126,217,?
Series pattern
2³+1,3³+1,4³+1,5³+1,6³+1
The answer is 7³+1= 344.
13. n³-1 Series :Each term is obtained by substracting 1 from the cube of a number.
Example:
i) 7,26,63,124,215,342,?.
The series is in the form 2³-1,3³-1,4³-1,5³-1,6³-1,7³-1
so the answer is 8³-1=511.
14. n³+n Series : Each term is a sum of a number with its cube.
Example:
i)2,30,130,?
Series pattern
1³+1,3³+3,5³+5
The answer is 7³+7=350.
15. n³-n Series : Each term is obtained by substracting 1 from the cube of a number.
Example:
i) 6,24,60,120,?
Series pattern
2³-2,3³-3,4³-4,5³-5
The Answer is 6³-6=210
16. Alternating Series : In which the successive terms increase and decrease alternatively.
Examples:
i) 1,4,27,16,125,36,?
The given series consists of cubes of odd numbers and squares of even numbers.
1³2²3³4²5³6²7³
So the missing term is 7³=343
ii)1,3,3,6,7,9,13,12,?
The given series is combination of two series
1,3,7,13,? and 3,6,9,12
First series followed in +2,+4,+6,+8
So the missing term is 13+8=21
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