Question

Find the number which does not fit in the given series: $75,\,79,\,72,\,80,\,69,\,83,\,66,\,86$.
(A) $69$
(B) $72$
(C) $79$
(D) $83$

Answer 1

Hint: In the above question, first we have to identify the pattern in the above series. If we notice the above series, we will find that there are two series of arithmetic progression, one is an increasing A.P. and the second one is a decreasing A.P and we have to find which is the incorrect number which is not following the sequence.

Complete step-by-step answer:
In the above question, we have given a series $75,\,79,\,72,\,80,\,69,\,83,\,66,\,86$.
If we observe the above series, we will find that there are two sequences having alternate terms, one with an increasing A.P. and the second one is a decreasing A.P.
Series $1$:
$75,\,72,\,69,\,66$.
It is the first series in which numbers are decreasing A.P. with a common difference $ - 3$.
Series $2$:
$79,\,80,\,83,86$.
It is the second series in which numbers are increasing A.P. with a common difference $3$.
Therefore, $79$should be replaced by $77$to obtain the next alternate numbers as $80$.
Hence, $79$ does not fit in the given series.

So, the correct answer is “Option C”.

Note: There are some properties of arithmetic progression:
Property I: If a constant quantity is added to or subtracted from each term of an arithmetic progression (AP), then the resulting terms of the sequence are also in AP with the same common difference $\left( d \right)$.
Property II: In an arithmetic progression of a finite number of terms, the sum of any two terms equidistant from the beginning and the end is equal to the sum of the first and last terms.