Question #112784
What is the next number of this sequence 1,2,6,12,20,29?
1
Expert's answer
2020-04-30T18:38:35-0400

Answer: 39

Lets  write  following  sequence:B  =  1,4,6,8,9,10,...This  numbers  are  sequence  of  nonprime  numbers.And  our  sequence  A  =  1,2,6,12,20,29,x...  has  following  rule:AnAn1=Bn121  =  1                            62  =  4126=6                          2012=82920=9So,  x29=10  x=39Let's\;write\;following\;sequence:\\B\;=\;1,4,6,8,9,10,...\\This\;numbers\;are\;sequence\;of\;non-prime\;\\numbers.\\And\;our\;sequence\;A\;=\;1,2,6,12,20,29,x...\;\\has\;following\;rule:\\A_n-A_{n-1}=B_{n-1}\\2-1\;=\;1\;\;\;\;\;\;\;\;\;\;\;\;\;\;6-2\;=\;4\\12-6=6\;\;\;\;\;\;\;\;\;\;\;\;\;20-12=8\\29-20=9\\So,\;x-29=10\Rightarrow\;x=39


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