Question

Find the missing number in the following series: 2, 6, 14, 26
(a) 50
(b) 59
(c) 42
(d) 38

Answer 1

Hint: Here, first determine the general sequence, the logic behind the sequence which are in the form ${{n}^{th}}$ term, ${{\left( n-1 \right)}^{th}}$ term, ${{\left( n-2 \right)}^{th}}$ term,.... and so on. Then, use the suitable operations to find the missing number.

Complete step-by-step answer:
We have a series of numbers, 2, 6, 14, 26 in the form of ${{n}^{th}},{{\left( n-1 \right)}^{th}},{{\left( n-2 \right)}^{th}},.......$ terms and so on. In this, we need to find the missing number or the number which is next in the series.
To find the number next in series, you first need to determine the logic behind the series, which means, you need to find out how the series is constructed.
Let us consider the next number in the series as $x$. Therefore, the series changes to 2, 6, 14, 26, $x$.
Now, let us find the general sequence behind the series.
The difference between the first two numbers is 6 – 2 = 4.
The difference between the numbers 6 and 14 is 14 – 6 = 8.
Now, the difference between the numbers 14 and 26 is 26 – 14 = 12.
Here we can see that, the difference of the numbers in the series, ${{n}^{th}}$ and ${{\left( n-1 \right)}^{th}}$ term is the multiples of 4.
So, let us find the next multiple of 4 after 12, which is the number 16.
Therefore, the difference between the two numbers which are 26 and $x$, and $x > 26$,
$x- 26 = 16$
Adding 26 on both the sides of the equation, we get
$x- 26 + 26 = 16 + 26$
$x = 42$
Hence, the number missing in the series or next in the series is 42.

Note: Here, in this question, find the general form of sequence is important and students can often make mistakes. The general sequence can only be considered if and only if it satisfies every single number in the given series. The logic behind every number obtained should be identical.