(877) 999-2681  | BECOME A TUTOR | BECOME A STUDENT  |  Sign In
Search 70,377 tutors SEARCH
WyzAnt Tutoring Tutor Tutor United States

## Linguistic Tutoring (both English and French) and Music Lessons

### Denver, CO (80210)

 Travel Radius 20 miles Hourly Fee \$35.00 Discount \$29.75 - \$33.25 Save up to 15%
 Background Check Passed 3/10/2013 Your first hour with any tutor is always 100% refundable!

# Alaina's Responses in WyzAnt Answers

#### What is the next number in this sequence 3 -6 12 4 20 ?

What is the next number in this sequence of numbers: 3 -6 12 4 20 ?

Need rule, thank you!

+ more- less
Asked by Gia from Marlboro, NJ
00

These numbers are related in the following way, beginning with 3: First, we subtract 9 to get -6: 3 - 9= -6. Next, we add 18: -6 + 18= 12.  To get from 12 to 4, we subtract 8: 12 - 8 = 4, and to get from 4 to the final number of 20, we must add 16: 4 + 16= 20.  We need to examine the numbers that we add/take away in the sequence to find a pattern so we can predict the next number.

So, let's look at the relationship between the numbers we added and subtracted to get from 3 to -6, from -6 to 12, and so on.  First, we subtracted 9, then added 18, then subtracted 8, then added 16. Think of ways in which the numbers 9, 18, 8, and 16 are related.  If I start with 9, I have to multiply by 2 to get 18: 9 * 2= 18.  To get from the next number, 8, to the fourth in the sequence, 16, I must multiply by 2 again: 8 * 2=16.

Now, we know the relationship between 9 and 18, and the relationship between 8 and 16.  We still need to figure out why the pattern moves from adding 18 to subtracting 8.  To do this, I returned to my idea of multiplying by 2, which grouped our numbers as follows: 9 was related to 18, and 8 was related to 16.  We can see that 9 minus 1 equals 8 (9 - 1= 8).

So, let's say 9 is "x." The relationship between the numbers in the original sequence can be summed up as follows: First number in the sequence - x, + 2x, - (x-1), + 2(x-1).  Let's plug in 3 as the first number in the sequence and 9 as x to test our pattern: 3 - 9= -6.  -6 + 2(9)= -6 + 18= 12.  12 - (9-1)= 12 - 8= 4. 4 + 2(9-1) = 4+ 2(8) = 4 + 16= 20.  If we put those answers in order, we have 3, -6, 12, 4, 20: the original sequence!

Using the pattern we found in that equation, we can predict that the next number in the sequence would be related to 20 by subtracting (x-2), where x still equals 9, since in order to get 4 after 12 we had to subtract (x-1) from 12. So, 20 - (x-2) becomes 20 - (9-2) = 20 - 7= 13.  And there's our answer!

## Other Denver, CO Tutors

### Alaina's Hourly Rate

Hourly Fee: \$35.00

Save up to 15% with a discount package

Cancellation: 3 hours notice required

#### How do I receive a discount?

Save between 5 and 15% on tutoring by purchasing credit with one of our prepaid discount packages. You can buy one of our standard 5, 10 or 15% packages or customize your own package based on how much tutoring you need. The credit you purchase can be used towards any tutor at any time and does not expire. If you do not use the entire package, we will simply deduct what you did spend on tutoring from your original purchase price and give you a refund. Discount packages start as low as \$190.

Credit For Only You Save
\$200 - \$399 \$190 - \$379 5%
\$400 - \$999 \$360 - \$899 10%
\$1,000 + \$850 + 15%

Your first hour with any tutor is protected by our Good Fit Guarantee: You don't pay for tutoring unless you find a good fit!

## Background Check Status for Alaina O.

Alaina O. passed a background check on 3/10/2013. You may run an updated background check on Alaina once you send an email.