Question

What will be the missing term for a sequence $ 5,4,15,7,23,11,29,?,33 $ respectively.
(a) \[13\]
(b) \[16\]
(c) \[15\]
(d) \[14\]

Answer 1

Hint: The given problem revolves around the concepts of BODMAS. So, we will first analyze the difference between two consecutive, alternative terms in the sequence. Relating with the summation the desire that is missing value can be obtained.

Complete step-by-step answer:
Since, we have given the sequence as,
 $ 5,4,15,7,23,11,29,?,33 $
After observing the sequence or series very keenly, it seems that,
(In the first half)…
The sequence arranged alternatively that is $ 5,15,23,29,33 $ respectively has a significant arrangement
 $ \Rightarrow $ $ 5 $
Where, in the next corresponding (adjacent to $ 4 $ ) term
 $ 15 = 5 + 10 $
Similarly, for rest of the terms
 $
  23 = 15 + 8 \\
  29 = 23 + 6 \\
  33 = 29 + 4 \;
  $
Where, it seems that in this particular arrangement there exists \[\sum\limits_{5 = 4}^n {(5 + a)} \]rule where, a is the multiple of two at $ a = 10 $ in the first, decreasing with the multiple of two!
Similarly,
(In the second half)…
i.e. $ 4,7,11,? $
it seems that,
the difference between these alternate terms also has some distinct arrangement such as,
 $ \Rightarrow $ $ 4 $
Where, in the next corresponding (adjacent to $ 5 $ ) term
 $ 7 = 4 + 3 $
Hence, the next term exists similarly
 $ 11 = 7 + 4 $
Where, it seems that in this particular arrangement there exists $ \sum\limits_{n = 4}^n {(3 + 1)} $ rule in every corresponding term
 $ \therefore 11 + 5 = 16 $
So, the correct answer is “Option B”.

Note: One must know the basics of mathematics such as brackets (B), addition (A), subtraction (S), multiplication (M), dividation (D), etc. and solve as per BODMAS. Also, one should be able to analyze the sequence keenly. Wise attention is needed in this kind of problem particularly. We should take care of the calculations so as to be sure of our final answer.