Question

What will be the next number in the series $1,2,4,7,11,?$
$A)15$
$B)16$
$C)21$
$D)22$

Answer 1

Hint: First, we will need to know about the concept of finding the missing sequence numbers. Select the first $2$ numbers and then check the difference between them. Again, select the second and third numbers and check the difference between them. In this way, we are able to check all the differences of the given numbers. Hence once the difference is found it is easy to calculate the missing number.

Complete step-by-step solution:
Since from the given that we have the numbers as $1,2,4,7,11,?$ and now fix the unknown number as the variable $X$. Which rewritten as $1,2,4,7,11,X$
First, take the first two numbers $1,2$ and then check its difference with the use of subtraction of greater number with the smaller number, hence we have $2 - 1 = 1$
Take the second and third numbers $2,4$ and then check its difference with the use of subtraction of greater number with the smaller number, hence we have $4 - 2 = 2$
Take the third and fourth numbers $4,7$ and then check its difference with the use of subtraction of greater number with the smaller number, hence we have $7 - 4 = 3$
Take the fourth and fifth numbers $7,11$ and then check its difference with the use of subtraction of greater number with the smaller number, hence we have $11 - 7 = 4$
Hence if we see the difference values are $1,2,3,4$ and thus the next terms difference is $5$
Similarly, take the fifth and sixth numbers $11,X$ and then check its difference with the use of subtraction of greater number with the smaller number, hence we have $X - 11 = 5$
Further solving we get $X - 11 = 5 \Rightarrow X = 16$
Therefore, the missing number is $16$ and the sequence can be written as $1,2,4,7,11,16$
Therefore, the option $B)16$ is correct.

Note: In the given missing number series, we can sometimes find missing numbers at the beginning or at the end of the given series. The layout in the missing number series is similar to the wrong number series, we have to identify the rule.
Hence here in the given problem, the rule is to find the difference between the two numbers successively.
After that, we solved it very easily using the algebraic operations of addition and subtraction.