GATE CSE 2014 Set 3 | Question: GA-4

Question

Which number does not belong in the series below?

$\qquad2, 5, 10, 17, 26, 37, 50, 64$

• A. $17$
• B. $37$
• C. $64$
• D. $26$

Answer 1

If $\large a_1,a_2,a_3\ldots a{_n}$ is the series and $i = 1$ to $n,$ then the series is defined as $a_i=i{^2} + 1.$
i.e the $i^{\text{th}}$ term is $1$ plus the square of $i.$
Series will be as follows $:1^{2} +1 ,2^{2}+ 1,3^{2} +1,4^{2}+1\ldots n^{2} + 1$
$\qquad\qquad\qquad\qquad\quad\;\; 2,5,10,17,26,37,50,65$

Hence $64$ does not belong to the series.

Correct Answer: $C$

Comments

I could not find the series pattern.. but I observed here every even number is followed by a odd number... so 50 should have been followed by a odd number but 64 is a even!!... so I chose option (C).. anyway your solution is perfect!!

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Add consecutive odd number to previous number

2 + 3 = 5
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50
50 + 15 = 65

Answer 2

We can even do like this to the series, 2,5,10,17,26,37,50,64:-

5-2=3

10-5=5

17-10=7

26-17=9

37-26=11

50-37=13

64-50=14; Since, the difference of “difference of terms” varies by 2 but in last step, the difference varies by 14-13=1; so 64 is the answer of the above question.

Answer 3

 

2,5,10,17,26,37,50,64
(even),(odd),(even),(odd),(even),(odd),(even),(even).
so 50 is at even position then 64 should be odd number but 64 is even ...so 64 will be not be here