We have two responses for you

Hi,

Look at the difference between successive terms. For the sequence 1, 6, 16, 36, _ the differences are

6 - 1 = 5
16 - 6 = 10
36 - 16 = 20

So the sequence starts with 1 and then you add 5 to get 6 and after that you add twice what you added to get the previous term.

This is probably not the way your daughter would say it but the key is that what you add doubles each time.

For d) rather than adding to get the next term look at multiplying.

I hope this helps,
Penny

Hi Baffled,

You have different kinds of sequences, but the way first thing I try
is to look at the gaps between consecutive terms. If that doesn't
help, look at the gaps between the gaps, and the gaps between them....

a) 1, 6, 16, 36, _

6-1 = 5 and 16 - 6 = 10 and 36 - 16 = 20, so the first sequence of
gaps is 5, 10, 20. To me, that looks like it doubles each time, so I
think the next gap will be 40. This means the next term in the
original sequence will be 36 + 40 = 76.

b) 2, 6, 14, 30, _

First sequence of gaps: 4, 8, 16...hmmm....these could be doubling too!

c) 1, 8, 22, 50, _

First sequence of gaps: 7, 14, 28.

d) 3, 9, 27, _

First gaps: 6, 18. nothing obvious there.

Maybe we should just look at the original terms themselves! Aren't
they tripling (multiplied by three) each time?

e) 2, 7, 17, 37, _

Can you get this one now that I showed you how I solved the others?

Cheers,
Stephen La Rocque.