Find What's Next
How do you find what numbers come next in other types of sequences?
Goal:
Goal:
Some sequences use two different operations to get the terms, switching back and forth as the sequence continues. Look at this pattern: 12, 22, 19, 29, 26, 36, 33…
You might notice that the terms increase and then decrease. This is a sign that two different operations are being used. When the terms increase, it signals addition or multiplication. When the terms decrease, it means subtraction or division is being used.
In this pattern, how much did the second term (22) increase from the first term (12)? To find this out, do 22 - 12. The answer is 10, so you know that 10 was added to 12 to get 22.
From the second term (22) to the third term (19), there is a decrease, so do 22 - 19, which is 3.
Now, test this idea (add 10, subtract 3) to see if it works in the rest of the sequence.
In this sequence, the rule "add 10, subtract 3" does work for all of the terms! If you continue to follow this pattern, what will the next two terms be?
The next operation in the pattern is add 10, so 33 + 10 = 43. Then, 43 - 3 = 40. The next two terms are 43 and 40.