Question

Find The Missing Number ? 18,38,78,138,218,318,?, 578​

Answer 1

The missing number is 438.

The numbers given are said to be in a sequence where all the numbers are related to each other.

They are not a random set of numbers and are rather numbers that form a pattern.

There is said to be a pattern in each of the arriving number where one number is deduced from its previous number and the number that follows also retains this pattern.

The pattern of arrival of these numbers hence needs to be found out in-order to find the missing number which is derived based on this observed pattern.

The given series of numbers can either be in arithmetic, geometric or harmonic progression.

Here, the given set of numbers are said to be in arithmetic progression because there is a common difference between them.

These common differences again have a common difference between them. Hence, there are 2 layers to the series.

In the given progression the difference between each number is observed to be 20 plus the previous difference.

Thus, the difference between the numbers of the series is given below:

$38-18=20$

$78-38=40$

$138-78=60$

$218-138=80$

$318-218=100$

Thus, it can be seen that the differences are in multiples of the number 20.

$20\times1=20\\20\times2=40\\20\times3=60\\20\times4=80...$ and so on.

Each difference is a multiple of 20 added to value of the previous difference and thus by following this pattern we can say that the next in the series will be the next multiple of 20.

Hence the previous number must be added to 120 to get the value of the missing number.

The missing number is sixth in the series which means that it is the sixth multiple of 20 that is to be added to the previous number.

Thus we have:

$318+120=438$

Hence, this is the missing number of the series.

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Answer 2

The missing number is 438.

Given,

The sequence of numbers 18,38,78,138,218,318,?, 578​

To Find,

The missing number in place of ?

Solution,

This problem could be solved using a simple method.

The given sequence of numbers is 18,38,78,138,218,318,?, 578​.

By checking the difference between these numbers, we can see the following:

38 -  18 = 20

78 -  38 = 40

138 -  78 = 60

218 - 138 = 80

318 - 218 = 100

Hence, we can observe that the difference between each pair of consecutive numbers in this sequence are multiples of 20.

The next difference would be 120.

Hence, the missing number is 318 + 120 = 438.

The sequence of numbers becomes 18,38,78,138,218,318,438,578.

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