# Number Series Mathematics

Introduction: Objective questions are asked from the following two types of questions related to the number-class in competition exams-

1. The wrong number present in the given number-range has to be identified.
2. The next number of given number-range has to be determined.

Example 1. Which is the wrong number in the given series?

Here number 20 is wrong. So the number is 20 in place of 19.

Example 2. What will be the next term for the given number order?

3 12 30 66 138 …? …

Explanation: (3 × 2) + 6 = 12, (12 × 2) +6 = 30, (30 × 2) + 6 = 66, (66 × 2) + 6 = 138, ( 138 × 2) + 6 = 282

Therefore, the desired post = 282 Answer.

Types of Number Series

1. Power Series

(A) Square Series:

Identification: If all the terms of the given series are the square of some numbers or a number close to them, that series will be a square series.

Example 1. Which number is wrong in the given number series?

In this category, the first, third, fifth and seventh positions from left to right are the squares of 1, 1 + 2 = 3, 3 + 2 = 5 and 5 + 2 = 7 respectively, and second, fourth and sixth terms are the squares of : 4, 4 + 4 = 8 and 8 + 4 = 12 respectively. Hence the number 169 of this series is wrong.

Example 2. What will be the next term for the given number series?

The first number in each pair of this series is the square of the number, the second number is equal to the sum of the number of the square of the same number. So the next number will be 110.

(B) (cube series):

Identification: If all the terms of the given series are the cube of some numbers or a number close to them, that series will be a cube series.

Example: Which is the wrong term in the given series?

Here number 65 is wrong. So the number 64 will be in-place of 65.

(C) Square and cube addition series.

Identification: If the difference between the initial two terms in the given number-series is very less and the difference between the last two terms is very high, then it can be a square addition series or cube addition series.

Example 1. Which is the wrong number in the given series?

The number 103 is wrong, so instead of number 103, the number will be 88.

Example 2. What will be the next term for the given series ?

Hence, the next number is 1228.

Identification: If the difference between the first and last terms of the given series is not very high and the difference of two consecutive terms is same then that series could be a constant addition series.

Example: Which is the wrong term in the given series?

Number 154 is incorrect in this number series. Hence the number 153 will be in-place of 153.

(B) Addition Series (in increasing order):

Identification: If the difference between the first and last terms of the given number series is not very high and the difference between the two consecutive terms is in ascending order, then that series can be addition series (increasing order).

Example: Which is the wrong term in the given number series?

This number 36 is incorrect. Therefore, the number should be 37 instead of 36.

3. Multiplication Series.

(A) Constant Multiplication Series.

Identification: If the difference between the first and last terms of the given series is very high and the ratio of two consecutive posts is equal, that series can be a fixed multiplication chain.

Example: Which is the wrong term in the given number series?

This number 365 is wrong. Therefore, the number 375 will be there instead of number 365.

(B) Multiplication Series (In Increasing Order)

Identification: If the difference between the first and last terms of the given number-series is very high and the proportion of two consecutive terms is in ascending order, then it can be a multiplication series (in increasing order).

Example: Which number is wrong in the given number-series?

This number 270 number is incorrect. The number should be 236.25 in place of 270.

(A) Constant multiplication and Constant Addition Series:

Identification: If there is a big difference in the first and last terms of a number-series and in the first of two consecutive terms, By adding a certain number and multiplying by a certain number, the next term is received, then that series could be a constant multiplication and constant addition series.
Example: Which is the wrong term in the given series?

The number 48 is wrong. The number should be 47 instead of 48.

(B) Constant multiplication and increasing addition series

Identification: If there is a big difference in the first and last terms of a number-series and in the first of two consecutive terms are multiplied by a certain number and by adding the number in ascending order, respectively, the next term is received, then the series can be Constant multiplication and addition in the increasing order.

Example: Which is the wrong term in the given series ?

In this series, the number would be 35 in place of number 38. Hence the number 38 is incorrect.

(C) Increasing Multiplication and Constant Addition Series

Identification: If there is a big difference in the first and last terms of any number-term and in the first term of two consecutive terms, by multiplying the number in increasing order and by adding any constant, the next term is received, then the series can be multiplied in the increasing order and constant addition series.

Example: Which is wrong term in the given number series?

In this numerical series, the number is 17 in place of number 16. So the number 16 is wrong.

(D) Increasing Multiplication and Increasing Addition Series.

Identification: If the difference of first and last positions in any given number-series is very high and the first term of two consecutive terms is multiplying by increasing order, adding a number in increasing order the next term is received, then that series can be multiplication in increasing order and addition in increasing order.

Example: Which number is wrong in the given number-series?

In this number-series, the number 27 will be 37 in place of number. So the number 37 is wrong.

5. Multiplication and subtraction Series

Constant Multiplication and Constant Subtraction Series
Identification: If there is a big difference in the first and last terms of any given number-series and after subtracting a certain number and by multiplying a certain number in the first of two consecutive terms, the next numbers is received then that series can be Constant multiplication and Constant subtraction series.

Example: Which number is wrong in the given number-series?

In this number-series, the number 192 is wrong.

(B) Constant multiplication and increasing subtraction series:

Identification: If the difference of first and last terms in any given number-series is very high and the first term of two consecutive terms are multiplied by a certain number and subtract an increasing number, the next term is received then that series could be constant multiplication and increasing subtraction series.

Example: Which number is incorrect in number series?

In this number-series the number will be 38 instead of 39. So the number 39 is wrong.

(C) Increasing Multiplication and Constant Subtraction Series

Identification: If the difference between the first and last terms of any given number-series is very high and the first term of two consecutive terms is multiplied by increasing number and then by subtracting a certain number, the next term is received then that series can be Increasing Multiplication and constant subtraction series.

Example: Which number is wrong in the given number series?

In this number-series the number will be 68 instead of 67. So the number 67 is wrong.

(D) Increasing Multiplication and Increasing Subtraction Series

Identification: If the difference of first and last terms in any given number-series is very high, and the first term of two consecutive terms is multiplied by increasing numbers and then by subtracting increasing number the subsequent term is received, then that series can be Increasing multiplication and increasing subtraction series.

Example: Which is the wrong term in the given series?

In this number-series the number will be 1321 instead of 1325. So the number 1325 is wrong.

6. Multiplication and division Series)

Identification: If the difference of first and last terms in any given number-series is not very high and the second term is larger than the first term, the third term is smaller from the second term and the fourth term is higher than the third. It can be a multiplication and division series.

Example: Which is the wrong term in the given series?

In this number-series, the number will be 13.5 in place of 18.5. So the number 18.5 is wrong.

7. Division and Multiplication series

Identification: If the difference of first and last terms in any given number-series is less and the second term is less than the first term, the third term is higher than the second term and the fourth term is less than the third term. Then it could be Division and multiplication series.
Example: Which number is wrong in the given number series?

In this number-series, the number will be 96 in place of number 92. So the number 92 is wrong.

8. Alternate Series

Identification: If you add or subtract a certain number in the first, third, fifth and seventh positions of any given number-series, or by multiply or divide by the fixed number, the second, fourth, Sixth and eighth terms are received, and in the second, fourth and sixth positions, by adding or subtracting any fixed number or by multiplying or dividing by that fixed number, the third, fifth, and seventh positions are received respectively, Then it may be an alternate series.

Example 1. Which number is wrong in the given series?

In this series there should be number 13 instead of number 12. So the number 12 is wrong.

Example 2. Which is the wrong number in the given number series?

In this number-series there should be number 6 in place of number 4. So the number 4 is wrong.

9. Pair Series

Identification: If in the first, third and fifth positions of any given number-series, adding or subtracting a certain number or multiplying or dividing by the fixed number, the third, fifth, and seventh terms received respectively Or in the second, fourth and sixth positions, by adding or subtracting a certain number or by multiply or divide it by fixed number, if the fourth, sixth and eighth positions are received respectively, The Series could be Pair Series.

Example 1. Which is the wrong term in the given number series?

In this number series, the number 71 will be replaced by the number 74. So the number 71 is wrong.

Example 2. Which is the wrong term in the given series?

In this series there will be number 14 instead of number 10. So the number 10 is wrong.