1, -6, -9, 0, 45, 198, ?

What's the next number in this series?

1, -6, -9, 0, 45, 198, ?

View Answer

675.

-006 =+01*3+(-9)
-009 =-06*3+09
+000 =-09*3+27
+045 =+00*3+45
+198 =+45*3+63

-9, 9, 27, 45, 63 form an arithmetic sequence with common difference 18.

Therefore, the next number is 675=198*3+81.