Question

Find the missing number. 67, 68, 67, 71, 63, ?, 45. a)57 b)61 c)72 d)79

Answer 1

Answer:

67

Step-by-step explanation:

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Answer 2

Concept

Missing digits are digits omitted in a particular series of digits that have similar differences between them. The process of writing  missing values ​​is called finding similar changes between those numbers and filling the missing values ​​in specific rows and locations.

Given

We have been given a series of numbers 67, 68, 67, 71, 63, ?, 45.

Find

We are asked to determine the missing number which comes after 63 .

Solution

In the series we can see that 68 can be obtained by adding one to 67

and on subtracting one from 68 we get the third number which is 67 .

but the difference between 71 and 67 is 4  which we can write as $(2)^2$and the difference between 63 and 71 is - 8 which we can write as $-(2)^3$ .

Hence to form a pattern we will add $(1)^2$ and subtract $(1)^3$ then add $(2)^2$ and subtract $(2)^3$ similarly add $(3)^2$ and subtract $(3)^3$.

$67+1^2=68\\\\68-1^3=67\\67+2^2=71\\71-2^3=63\\63+3^2=72$

$72-(3)^3=45$

Therefore , the missing number is 72 which is option (c) .

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