Basic Concepts of Number Series with Examples

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Basic Concepts of Number Series with Examples

Basic Concepts of Number Series with Examples

Number Series is an arrangement of numbers according to certain rule or pattern. In a number series, each number is called ‘Term’ of the series. In an Number Series question, you typically need to identify the,

  • Next number in a given number series.
  • Missing number in a given number series.
  • Incorrect number in a given number series.

Solving Problems Based on Number Series

Step-I: Observe if there are there any familiar numbers in the given series. For example familiar numbers are Primes Numbers, Perfect Squares, Cubes. Such numbers are very easy to identify.

Step-II: Calculate the differences between the numbers. Observe the pattern in the differences. If the differences are growing rapidly it might be a Square Series, Cube Series, or Multiplicative Series. If the numbers are growing slowly it is an arithmetic series. If the differences are not having any pattern then

  1. It might be a double or triple series. Here every alternate number or every 3rd number form a series.
  2. It might be a sum or average series. Here sum of two consecutive numbers gives 3rd number or average of first two numbers gives next number.

Step-III: Sometimes number will be multiplied and will be added with another number, so we need to check such patterns.

Prime Number Series

Example-I: 2, 3, 5 ,7, 11, 13, ….
Answer: The given series is prime number series. The next prime number is 17.

Example-II: 2, 5, 11, 17, 23, …., 41.
Answer: The alternate prime numbers are written. The primes after 23 are 29, 31, 37 and 41. So, based on the pattern the answer is 31.

Difference Series

Example-I: 2, 5, 8, 11, 14, 17, …., 23.
Answer: The difference between the numbers in ascending order is 3.
∴ the next term is (17+3 = 20).

Example-II: 45, 38, 31, 24, 17,…, 3.
Answer: The difference between the numbers in descending order is 7.
∴ the next term is (17-7=10)

Multiplication Series

Example-I: 2, 6, 18, 54, 162, …., 1458.
Answer: Each term is multiplied by 3 to get next term.
∴ The next term is (162×3 = 486).

Example-II: 3, 12, 48, 192, …., 3072.
Answer: Each term is multiplied by 4 to get the next term.
∴ the next term is(192×4 =768).

Division Series

Example-I: 720, 120, 24, …, 2, 1
Answer: 720/6=120, 120/5=24, 24/4=6, 6/3=2, 2/2=1.
∴ The answer is 6.

Example-II: 32, 48, 72, 108, …., 243.
Answer: Number × 3/2 = Next Number. 32×3/2=48, 48×3/2=72, 72×3/2=108, 108×3/2=162, 162×3/2=243.
∴ The answer is 162.

‘n’ Square Series

Example-I: 1, 4, 9, 16, 25, …., 49
Answer: The series is 12, 22, 32, 42, 52
∴ The next number is 62=36;

Example-II: 0, 4, 16, 36, 64, …., 144.
Answer: The series is 02,22,42,62,82 etc.
∴ The next number is 102=100.

‘n’ Square Variants

n2−1 Series

Example: 0, 3, 8, 15, 24, 35, 48, ….
Answer: The series is 12−1,22−1,32−1,42−1,52−1,62−1,72−1 etc.
∴ The next number is 82−1=63.

Another Logic: Difference between numbers is 3,5,7,9,11,13 etc. The next number is (48+15=63).
Remember logic can be different, however answer should be the same.

n2+1 Series

Example: 2, 5, 10, 17, 26, 37, …., 65.
Answer: The series is 12+1, 22+1, 32+1, 42+1, 52+1, 62+1 etc. The next number is 72+1=50.

n2+n Series (or) n2−n Series

Example: 2, 6, 12, 20, …., 42.
Answer:
Logic-I: The series is 12+1, 22+2, 32+3, 42+4 etc. The next number = 52+5=30.
Logic-II: The series is 1×2 ,2×3, 3×4, 4×5, The next number is 5×6=30.
Logic-III: The series is 22−2,32−3,42−4,52−5, The next number is 62−6=30

‘n’ Cube Series

Example: 1, 8, 27, 64,125, 216, ….
Answer: The series is 13, 23, 33, 43, 53, 63, etc. ?
The missing number is 73=343.

‘n’ Cube Variants

n3+1 Series or n3−1 Series

Example-I: 2, 9, 28, 65, 126, 217, 344, ….
Answer: The series is 13+1,23+1,33+1, etc.
∴ The missing number is 83+1=513.

Example-II: 0, 7, 26, 63, 124, …., 342.
Answer: The series is 13−1, 23−1, 33−1 etc
∴ The missing number is 63−1=215.

‘n’ Cube Variants

n3+n Series or n3−n Series

Example 1: 2, 10, 30, 68, 130, …., 350.
Answer: The series is 13+1, 23+2, 33+3, 43+4, 53+5, ? , 73+7 etc. ?
The missing number is 63+6=222.

Example-II: 0, 6, 24, 60, 120, 210, ….
Answer: The series is 13−1, 23−2, 33−3, 43−4, 53−5, 63−6, etc. ?
the missing number is 73−7=336.

n3+n Series or n3−n Series

Example-I: 2, 12 ,36, 80, 150, ….
Answer: The series is 13+12, 23+22, 33+32, 43+42, 53+52, etc.
The missing number is 63+62=252

Example-II: 0, 4, 18, 48, 100, ….
Answer: The series is 13−12, 23−22, 33−32, 43−42, 53−52, etc.
The missing number is 63−62=180

ab, a + b Series

Example: 48,12,76,13,54,9,32,…, where a and b are digits of a number
Answer: 4+8=12, 7+6=13, 5+4=9, 3+2=5.

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