Question

Complete the given sequence 4, 2, 5, 4, 7, 6, 10, 8, 14?

Answer 1

Hint: Consider the odd terms and even terms of the sequence separately. Thus find the number after separating the sequence accordingly.

Complete step-by-step answer:
Consider the given sequence we got 4, 2, 5, 4, 7, 6, 10, 8, 14, _
The digits are jumbled and they are not in an ascending or descending order. Let us look at the odd terms first of the given series.
4, 2, 5, 4, 7, 6, 10, 8, 14, _
To make it easy, we can make them as,
\[\overset\frown{4,2,5}\overset\frown{,4,7}\overset\frown{,6,10}\overset\frown{,8,14}\overset\frown{,\_}\]
Thus from the above the odd terms are 4, 5, 7, 10, 14, _.
Here difference between the numbers are 1, 2, 3, 4 etc i.e. we can write it as,
\[\]
Thus we can guess the next number after 14 as 19. But 19 is not our required number.
4, 2, 5, 4, 7, 6, 10, 8, 14, _, 19
Now let us consider the even digits of the given sequence.
\[4,\]
Thus from the above the even terms are 2, 4, 6, 8, _. From this we can say that they are a multiple of 2.
\[\begin{align}
  & 2\times 1=2 \\
 & 2\times 2=4 \\
 & 2\times 3=6 \\
 & 2\times 4=8 \\
 & 2\times 5=10 \\
\end{align}\]
Thus we got the next number of the sequence as 10.
So, we can complete the series as,
4, 2, 5, 4, 7, 6, 10, 8, 14, 10
Hence we have completed the given sequence and the missing number is 10.
4, 2, 5, 4, 7, 6, 10, 8, 14, 10

Note: We need not write many steps to complete the series. We can write these both steps together.
\[\overbrace{4,2,5}^{+1}\overbrace{,5,7}^{+2}\overbrace{,6,10}^{+3}\overbrace{,8,14}^{+4}\overbrace{,\underline{10},19}^{+5}\]
\[4,\underbrace{2,5,4}_{+2}\underbrace{,7,6}_{+2}\underbrace{,10,8}_{+2},\underbrace{14,\underline{10}}_{+2},19\]
Thus we can easily identify the next number.