What is the next number in the sequence 3,9,-1,-4,-15

Johnny R.,

Great observation!

You can use integer function to get a recursive form.

3, 9 , -1, -4, -15

t(1) = 3

t(n) = t(n-1) * [int(n/2)+2], if n is even.

t(n) = t(n-1) - [int(n/2)+9], if n is odd.

Check:

t(1) = 3

t(2) = 3*(1+2) = 9

t(3) = 9 - (1+9) = -1

t(4) = (-1)*(1+4) = -4

t(5) = (-4) - (2+9) = -15

t(6) = (-15)(3+2) = -75

t(7) = -75 - (3+9) = -87

t(8) = (-87)(4+2) = -522

......

The pattern that I see with this number sequence is alternating subtraction and multiplication.  You perform the operations in alternating order.  When you perform subtraction you increase the subtrahend by 1. When you perform multiplication you increase the multiplier by 1.

  Here is the sequence

3 x 3 =  9

9-10 =  -1

-1 x 4 = -4 (multiplication, increasing multiplier by 1) 

-4 - 11 = -15(subtraction, increasing subtrahend by 1)

-15 x 5 = -75 (multiplication, increasing multiplier by 1)

-75 - 12 = -87(subtraction, increasing subtrahend by 1)

-87 x 6 = -522 (multiplication, increasing multiplier by 1)

-522 - 13 = -535(subtraction, increasing subtrahend by 1)

Utilizing this pattern the next 4 numbers in the sequence would be -3745,-3759,-30072,-30087

Therefore the sequence would be:

3, 9. -1, -4,-15,-75, -87, -522, -535, -3745, -3759, -30072, -30087

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This is tough. It increases once, then decreases 3 times. Can you double check to make sure these are typed in the correct order? Also, it might be helpful if you provided the name of your class, and  the names of the chapter/section you guys are on,  when this problem was given to you.

I'll keep working on this in in the meantime.