To find a missing number in a Sequence, first we must have a Rule
Sequence
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A Sequence is a set of things (usually numbers) that are in order.
Each number in the sequence is called a term (or sometimes 'element' or 'member'), read Sequences and Series for a more in-depth discussion.
Finding Missing Numbers
To find a missing number, first find a Rule behind the Sequence.
Sometimes we can just look at the numbers and see a pattern:
Example: 1, 4, 9, 16, ?
Answer: they are Squares (12=1, 22=4, 32=9, 42=16, ..)
Rule: xn = n2
Sequence: 1, 4, 9, 16, 25, 36, 49, ..
Did you see how we wrote that rule using 'x' and 'n' ?
xn means 'term number n', so term 3 is written x3
And we can calculate term 3 using:
x3 = 32 = 9
We can use a Rule to find any term. For example, the 25th term can be found by 'plugging in' 25 wherever n is.
x25 = 252 = 625
How about another example:
Example: 3, 5, 8, 13, 21, ?
After 3 and 5 all the rest are the sum of the two numbers before,
That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence:
3, 5, 8, 13, 21, 34, 55, 89, ..
Which has this Rule:
Rule: xn = xn-1 + xn-2
Now what does xn-1 mean? It means 'the previous term' as term number n-1 is 1 less than term number n.
And xn-2 means the term before that one.
Let's try that Rule for the 6th term:
x6 = x6-1 + x6-2
x6 = x5 + x4