Question

The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34……….... Is said to be in…………...
a) Arithmetic progression
b) Finite sequence
c) Fibonacci sequence
d) None of the above

Answer 1

Hint: For solving this problem, we individually consider all the options one by one by applying the suitable condition in the given sequence respective to that option. After analysing all the options, we will get our potential answer.

Complete step-by-step answer:
According to the problem statement, we are given a sequence 1, 1, 2, 3, 5, 8, 13, 21, 34………....
Now, considering the first option which is arithmetic progression, the common difference should remain constant. So, the common difference of the series:
$\begin{align}
  & {{d}_{1}}={{a}_{2}}-{{a}_{1}} \\
 & \Rightarrow 1-1=0 \\
 & {{d}_{2}}={{a}_{3}}-{{a}_{2}} \\
 & \Rightarrow 2-1=1 \\
 & \therefore {{d}_{2}}\ne {{d}_{1}} \\
\end{align}$
Hence, option (a) is incorrect.
Considering the second option which is a finite sequence. We observe that in our sequence the upcoming number is the sum of previous two numbers. So, it can come under finite sequence if no other option is correct.
Now, considering the third option which is Fibonacci series. The definition of Fibonacci series exactly matches with the given sequence which states that the upcoming number is the sum of previous two numbers. So, this is the required option.
Therefore, option (c) is correct.

Note: Students must check all the options individually. Common mistake which is bound to occur is the selection of option (b) without considering the option (c) due to impulsive response. This approach will lead to selection of incorrect answers.