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Find the Sum of First 60 Natural numbers

  • Last Updated : 03 Sep, 2021
Geek Week

Numerals are the mathematical figures used in financial, professional as well as a social field in the social world. The digits and place value in the number and the base of the number system determine the value of a number. Numbers are used in various mathematical operations as summation, subtraction, multiplication, division, percentage, etc. which are used in our daily businesses and trading activities.

What are numbers?

Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc. which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system.

Numbers generally also known as numerals are the mathematical values used for, counting, measurements, labeling and measuring fundamental quantities.

Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2,4,7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.



Types Of Numbers

There are different types of numbers categorized into sets by the number system. The types are described below:

  • Natural numbers: Natural numbers are the positive counting numbers that count from 1 to infinity. The subset doesn’t include fractional or decimal values. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N=1,2,3,4,5,6,7,……………
  • Whole numbers: Whole numbers are positive natural numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set can be represented as W=0,1,2,3,4,5,………………
  • Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z’. The set of integers can be represented as Z=………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….
  • Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can also be expressed in the fractional form in some cases. It can be expressed as 2.5,0.567, etc.
  • Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
  • Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
  • Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
  • Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.

What are Whole Numbers?

The whole numbers are the numbers without fractions and are a collection of positive integers from 0 to infinity. All the whole numbers exist in number lines. All the whole numbers are real numbers but we can’t say that all the real numbers are whole numbers. Whole numbers cannot be negative. The whole numbers are represented by the symbol “W”.

Examples of whole Numbers

0, 15, 16, 76, and 110, etc. all are examples of whole numbers.

How to Find Sum of whole numbers?

There are multiple methods to find the sum of numbers in a range. Following are some of these methods:

Method 1: Manually adding the sum of each number with the number next to it and computing the final sum.

For ex: 1 + 2 + 3 + 4 + 5 = 15

Method 2: Using the formula of adding terms of Arithmetic Progression



Sn = n/2[2a + (n-1)d]

Here, 

n = Number of terms,

a = first term of A.P.

d = common difference between terms

Method 3: Using the formula of adding terms using first and last terms

Sn = n/2[a+l]

Here, 

n = Number of terms

a = first term of A.P.

l = last term of the A.P.

Find the sum of 1 + 2 + 3 + … + 60.

Answer:

The above-given series is in an Arithmetic form with a common difference of 1. The sum of numbers from 1 to 60 can be calculated with the help of the following methods:

Method 1: Manually adding: 

1 + 2 + 3 + 4 + 5 + … + 58 + 59 + 60 = 1890

Method 2: Using A.P. Sum formula:

Sn = n/2[2a + (n-1)d]

Here in the question, 

n = 60, a = 1, and d = 1

Therefore, 



Sn = 60/2[2 × 1 + (60 – 1) × 1]

    = 30[2 + 59]

    = 30 × 61

    = 1830

Method 3: Using first and last terms

Sn = n/2[a+l]

Here, n = 60, a = 1, and l = 60

Therefore, 

Sn = 60/2[1+60]

     = 30 × 61

     = 1830

Similar Questions

Question 1: Find the Sum of 1 + 2 + 3 + 4 + 5 + 6 + 7

Answer:

Sum of the above series will be 28.

Question 2: Find the sum of first 10 integers?

Answer:

The sum of first 10 integers will be calculated using AP sum formula:

Sn = n/2[a + l]

     = 10/2[1 + 10]

     = 5 × 11

     = 55

Question 3: Find the sum of the first 50 numbers.

Answer:

The sum of first 50 integers will be calculated using AP sum formula:

Sn = n/2[a + l]

    = 50/2[1 + 50]

    = 25 × 51

    = 1275

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