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This question already has an answer here:

enter image description here

Question 1 => what is the pattern of this image?
Question 2 => what is the source to become 42 at last?

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marked as duplicate by Ian MacDonald, DrunkWolf, Novarg, Irishpanda, Deusovi Dec 16 '15 at 13:51

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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I don't want to make it complicated. It's pretty simple.

Series goes like this

n * (n+1)

So,

2 * 3 = 6

3 * 4 = 12

4 * 5 = 20

5 * 6 = 30

6 * 7 = 42

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1
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If we call the left series $L(n)$ and the right series $R(n)$, then

$L(n) = n$, and $R(n)=R(n-1)+2*L(n)$.

This simplifies to

$R(n) = 2\sum\limits_{i=1}^ni = (n+1)*n$

If your second question is asking about what R(7) will be then it's

$R(7) = 8*7 = 56$

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  • $\begingroup$ Hi. Your answer looks genius. The question is not made by me. So actually, according to the source, I just ticked Nivin answer as right and simple as its question. Your answer is also right and really looked cool. Thank you for answering!! $\endgroup$ – Nai Dec 17 '15 at 3:27
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a = b

c = d

e = f

on the left part you just add one on each line. The result is the current number * the number just under (like b = ac, d = ce )

and i didn't undertsand your last question :)

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  • $\begingroup$ well i actually revealed the pattern with words, it is basically x = n *n+1 $\endgroup$ – JohnnyBgud Dec 16 '15 at 15:29
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    $\begingroup$ I had to read your answer three times to make any sense of it. A well-written answer should be understandable the first time I look through it. $\endgroup$ – mmking Dec 16 '15 at 15:45
  • $\begingroup$ Thank you for answering. As it is a little complicated way of answering, though I understand, it is hard to tick as right and best answer. :D Thanks again! $\endgroup$ – Nai Dec 17 '15 at 3:23
  • $\begingroup$ I tried my best since i'm not that good in english i am sorry, at least i tried to participate ^^ $\endgroup$ – JohnnyBgud Dec 17 '15 at 7:35
  • $\begingroup$ Yes @JohnnyBgud being participated is important! I get into other questions like that too :D $\endgroup$ – Nai Dec 22 '15 at 5:43
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Question 1 - The number on the right side is the product of the number on the left and the next whole number in sequence. I.e 2*3, 3*4, 4*5

Question 2 - The next step in the sequence is 7=56

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    $\begingroup$ Thank you for answering. I have ticked Nivin's as the right answer as it is more simple to look at it once. For you answer, you mis-understood my Question 2, I was just asking for answer 6*7 = 42. Thank you again! $\endgroup$ – Nai Dec 17 '15 at 3:21

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