SOLUTION: find next term 16,12,28,8,4?? plz explain ans is 40 but how??

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Question 949999: find next term 16,12,28,8,4?? plz explain ans is 40 but how??
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
We build the sequence out of this arithmetic sequence 

S = 16,12,8,4,0,-4,-8,-12,-16,-20,...

------------------------------------------

Take the first two terms of the arithmetic sequence S, 16 and 12

Sequence is now: 16, 12

Add the last 2 terms, 16+12 = 28

Sequence is now: 16,12,28

Take the next two terms of the arithmetic sequence S, 8 and 4

Sequence is now: 16,12,28,8,4

Add the last 3 terms, 28+8+4 = 40

That's the answer and a pattern that works.  
Just for fun, let's continue the pattern
a few more times:

--------------------------

Take the next two terms of the arithmetic sequence S, 0 and -4

Sequence is now: 16,12,28,8,4,40,0,-4

Add the last 4 terms, 4+40+0-4 = 40

Sequence is now: 16,12,28,8,4,40,0,-4,40

Take the next two terms of the arithmetic sequence S, -8 and -12

Sequence is now: 16,12,28,8,4,40,0,-4,40,-8,-12

Add the last 5 terms, 0-4+40-8-12 = 16

Sequence is now: 16,12,28,8,4,40,0,-4,40,-8,-12, 16

Take the next two terms of the arithmetic sequence S, -16 and -20

Sequence is now: 16,12,28,8,4,40,0,-4,40,-8,-12,-16,-20 

Add the last 6 terms, -4+40-8-12-16-20 = -20

Sequence is now: 16,12,28,8,4,40,0,-4,40,-8,-12, 16, -20

That's enough!

Edwin
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