Brain Teasers
1, -6, -9, 0, 45, 198, ?
What's the next number in this series?
1, -6, -9, 0, 45, 198, ?
1, -6, -9, 0, 45, 198, ?
Hint
1 is not divisible by 3, -6 is only divisible by 3 but not by 9. Therefore, consider multiplying by 3.Answer
675.-6=1*3+(-9)
-9=-6*3+9
0=-9*3+27
45=0*3+45
198=45*3+63
-9, 9, 27, 45, 63 form an arithmetic sequence with common difference 18.
and therefore, the next number is
675=198*3+81.
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