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Replace the question mark and explain the rule behind this sequence:

5, 12, 24, 36, 52, 68, 84, 100, ?

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2 Answers 2

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The next term is:

120

Because the terms are all:

The sum of the next 2 consecutive prime numbers:

2+3=5,
5+7=12,
11+13=24,
17+19=36,
23+29=52,
31+37=68,
41+43=84,
47+53=100

Meaning that the next term must be:

59+61=120

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  • $\begingroup$ I feel like this question is a duplicate of an existing one, but a quick search before posting did not reveal an appropriate question... Happy to stand corrected if anybody finds one! :) $\endgroup$
    – Stiv
    Dec 1, 2019 at 12:11
  • $\begingroup$ Yes, 120 is correct. I think you might refer to my previous post which also consisted of prime numbers. They were similar but not the same. $\endgroup$ Dec 1, 2019 at 12:27
  • $\begingroup$ @Prim3numbah That may be it - the multiplication one... $\endgroup$
    – Stiv
    Dec 1, 2019 at 12:28
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119? With regard to the main increase amount (ie 7, 12, 16), change of +5 then 0 repeated x 1, change of +4 then 0 repeated x 3, change of 3 then 0 repeated x 5. With the zero repetition being increasing odd numbers and the main increasing amount reducing by 1 each round.

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  • $\begingroup$ I see. But no, its not correct. $\endgroup$ Dec 1, 2019 at 11:48

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