0

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

can't find a pattern. can you help

### 3 Answers by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
2

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

......

Johnny R. | Exceptional Math and Accounting TutorExceptional Math and Accounting Tutor
4.8 4.8 (162 lesson ratings) (162)
0

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

-

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 = -522

Thus the remainder of the problem needs to be adjusted.

James P. | Slightly Epic Math TutoringSlightly Epic Math Tutoring
5.0 5.0 (5 lesson ratings) (5)
0

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.