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 Hint: Assume the four consecutive even numbers as: - ‘x’, ‘x + 2’, ‘x + 4’ and ‘x + 6’. Take the sum ofthese four numbers. Now find the average by using the formula: - Average = (sum of observations) /(number of observations). Equate this average with 27 to form a linear equation in one variable, which is‘x’. Solve this equation to get the value of ‘x’ and substitute it in ‘x + 6’ to get the correct answer. Complete step by step answer: We have been given that the average of four consecutive even numbers is 27, and we have to find thelargest number.Let us assume the four consecutive even numbers as: -‘x’, ‘x + 2’, ‘x + 4’ and ‘x + 6’.Adding these four numbers, we get,Sum = \[x+\left( x+2 \right)+\left( x+4 \right)+\left( x+6 \right)\]Sum = 4x + 12Sum = 4 (x + 3)Now, let us find the average. We know that,Average = (sum of observations) / (number of observations)Therefore, applying the above formula, we have,Average = \[\dfrac{4\left( x+3 \right)}{4}\]\[\Rightarrow 27=\dfrac{4\left( x+3 \right)}{4}\]By cross multiplication, we get,\[\Rightarrow 27\times 4=4\left( x+3 \right)\]Cancelling the common factors, we have,\[\begin{align}& \Rightarrow 27\times 1=\left( x+3 \right) \\& \Rightarrow 27=x+3 \\& \Rightarrow x=27-3 \\& \Rightarrow x=24 \\\end{align}\]Therefore, substituting the value of ‘x’ in all the assumed even numbers, we get,\[\begin{align}& \Rightarrow x=24 \\& \Rightarrow x+2=26 \\& \Rightarrow x+4=28 \\& \Rightarrow x+6=30 \\\end{align}\]Clearly, we can see that the largest of these numbers is ‘x + 6’ or 30.So, the correct answer is “Option D”. Note: You may note after assuming ‘x’ as the first even number we have assumed the second even number as ‘x + 2’ and not ‘x + 1’. This is because, as ‘x’ is even, therefore ‘x + 1’ will be odd and so itcannot be considered as the next even number. Also, note that after getting the values of ‘x’ we have tocheck the greatest or smallest number by substituting the values of ‘x’ in the assumed numbers.
Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written in a series where the difference between the numbers is fixed and where no numbers are skipped in between. Let us learn more about consecutive numbers in this article. What are Consecutive Numbers?To understand consecutive numbers, we first need to understand the concept of predecessors and successors. The number that is written immediately before a number is called its predecessor. The number that is written immediately after a number is called its successor. For example, consider the list of natural numbers,1, 2, 3, 4, and 5. The predecessor of 2 is 1, and the successor of 2 is 3. Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. They usually have a difference of 1 between every two numbers. Note that the difference between any predecessor-successor pair is fixed. Let us look at a few examples of consecutive numbers. In the above example, the difference between any predecessor-successor pair is 1. If we denote the 1st number as n, then the consecutive numbers in the series will be n, n+1, n+2, n+3, n+4, and so on. Consecutive Even NumbersWe know that even numbers are those numbers that end in 0, 2, 4, 6, and 8. Now, let us consider the set of even numbers from 2 to 12 and write them in ascending order. The numbers are arranged as 2, 4, 6, 8, 10, 12 when written from the smallest to the largest. We can see that the difference between any predecessor-successor pair is 2. Therefore, these numbers form the list of consecutive even numbers. Consecutive Odd NumbersWe know that odd numbers are those numbers which cannot be completely divided by 2. When we arrange them in ascending order, we can see that the difference between them is always 2. For example, the numbers 3, 5, 7, 9, and 11 are called consecutive odd numbers because the difference between any predecessor-successor pair is 2, like, 5 - 3 = 2 and 7 - 5 = 2. Properties of Consecutive NumbersConsecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The following points show the properties of consecutive numbers.
Consecutive Numbers FormulaFor a number n, the next two consecutive numbers are (n + 1) and (n + 2). Given below are more consecutive number formulas.
Important PointsHere is a list of some important points that should be remembered while working with consecutive numbers.
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FAQs on Consecutive NumbersConsecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers. What are Consecutive Positive Numbers?Consecutive positive numbers are the set of positive numbers whose difference is 1. For example, 1, 2, 3, 4, 5, 6 ... is the set of consecutive positive numbers. Can Consecutive Numbers be Decimals?No, consecutive numbers cannot be decimal numbers because there are several numbers between every two decimal numbers. For example, in the list of these numbers: 3.1, 3.2 and 3.3..., many decimal numbers like 3.11, 3.111, 3.1111... exist between them. When are 2 Numbers Considered Consecutive Numbers?Two numbers that follow each other in order are called two consecutive numbers. For example:
What are Odd Consecutive Numbers?We know that odd numbers are those numbers which are not completely divisible by 2. When we arrange odd numbers in ascending order, we can see that the difference between them is always 2. Therefore, when odd numbers are arranged as 3, 5, 7, 9, and 11, they are called consecutive odd numbers because these numbers have a fixed difference of 2 between any predecessor-successor pair. What are Non Consecutive Numbers?Non consecutive numbers are those numbers that form a list in which there is no pattern or any fixed difference between a predecessor and a successor. For example, 2, 5, 17, 21 and so on are non consecutive numbers. Can Consecutive Numbers be Fractions?No, just like decimals, fractions cannot be considered as consecutive numbers because there are several fractions existing in between two fractions. |
The average of five consecutive even numbers is 26 when five numbers are written in ascending order
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