Dear Math Central,

My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help!

10, 14, 18, 22, _, _, _.

12, 21, 39, 75, _, _, _.

Thanx so much!
-Steph

Hi Stephanie,

In these problems you have to look for patterns. You need to see how each term is generated from the previous terms. Sometimes the pattern is easy to spot. For example in

1, 3, 5, 7, _, _, _. Each term is the previous term plus 2 so the next three terms would be 9,11 and 13. Also in the sequence

2, 4, 8, 16, _, _, _. each term is twice the previous term so the next three terms are 32,64 and 128.

In your first sequence, if you find the differences they are

14 - 10 = 4
18 - 14 = 4
22 - 18 = 4. Thus each term is 4 more than the previous term. Thus the next three terms are

22 + 4 = 26
26 + 4 = 30
30 + 4 = 34

In the second sequence the differences are

21 - 12 = 9
39 - 21 = 18
75 - 39 = 36. Here the differences are doubling each time. Thus the next three differences are 72,144 and 288. Hence the next three terms are

75 + 72 = 147
147 + 144 = 291
291 + 288 = 579

Now try the rest of the problems.

Penny
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