SOLUTION: What is the missing number at the beginning of this sequence? and how do you work it out? _, 5, 9, 26, 103

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Question 979573: What is the missing number at the beginning of this sequence? and how do you work it out?
_, 5, 9, 26, 103

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
What is the missing number at the beginning of this sequence? and how do you
work it out?
_, 5, 9, 26, 103
--------------
Here's the strategy I used:

Since the unknown is at the first, I decided I'd start with 103 
and go backwards.

I noticed that 103/26 = 3.96...

So I thought "That's real close to 4"

Then I asked "What is 4x26?". It's 104.

That's 1 more than 103.

So to get from 103 to 26:

103, add 1, then divide by 4.

I thought about doing the same to get from 26 to 9

Then I noticed that 26/9 = 2.889...

So I thought "That's real close to 3"

So I thought "What is 3x9?" It's 27.

That's 1 more than 26.

So to get from 26 to 9:

26, add 1, then divide by 3.

So I got a pattern!  I then checked to see if it 
works to get from 9 to 5

9, add 1, then divide by 2.  Yes, 9+1=10 and 10/2 = 5

So to get the missing first term:

5, add 1, then divide by 1. So, 5+1=6 and 6/1 = 6.

So the answer is 6.

----

Check it, reversing the pattern, going forward:

6, multiply by 1, get 6, subtract 1, get 5.
5, multiply by 2, get 10, subtract 1, get 9.
9, multiply by 3, get 27, subtract 1, get 26.
26, multiply by 4, get 104, subtract 1, get 103.

Somebody else might have used a different strategy, but that's
the way I approached it.

Edwin

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