Question

What is the pattern in the sequence $\text{1 2 4 3 6 8 7 14 16}$ ?

Answer 1

Hint: Here in this question we have been asked to find the pattern involved in the given sequence $\text{1 2 4 3 6 8 7 14 16}$ . For answering this question we will analyse the relation between the consecutive terms in the sequence.

Complete step by step solution:
Now considering the question we have been asked to find the pattern involved in the given sequence $\text{1 2 4 3 6 8 7 14 16}$.
By analysing the given sequence $\text{1 2 4 3 6 8 7 14 16}$ we can say that the pattern involved for first four terms is:
The second term is equal to the doubled first term $ 2=1\times 2$ .
The third term is equal to the sum of the second term and two $ 4=2+2$ .
The fourth term is equal to the third term less than one $ 3=4-1$ .
The same pattern repeats for the next three terms also.
The fifth term is doubled, the fourth term $ 6=3\times 2$ and the sixth term is the sum of the fifth term $ 8=6+2$ and two and the seventh term is the sixth term less than one $ 7=8-1$ .
Therefore we can conclude that the pattern involved can be simply represented as double, add 2, subtract 1.
The next term of the sequence will be $15$ .

Note: While answering questions of this type we should be very careful. Generally the solution doesn't strike easily but practice of questions like this helps us to improve our performance. Someone can consider the third term as the double of the second term but it doesn’t obey while proceeding to higher terms.