can't find a pattern. can you help

can't find a pattern. can you help

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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**

** **

** **

**
**-

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

Justin H.

Math, Computer Science, and SAT Tutoring from a Google Engineer

New York, NY

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Adam B.

PhD physicist teaching math and science

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## Comments

Hi Jonny.

This makes sense except for the fact that the multiplier should be "6" for this line as "5" has already been used:

-87 x

5 = -522 (multiplication, increasing multiplier by 1)should be

-87 X 6 = -522Thus the remainder of the problem needs to be adjusted.