According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid.
The simplest pattern is Un = 2*n for n = 1, 2, 3, ...
+2
4*2-2=6 6*2-2=10
(n - 10) + 6
Keep subtracting 6
Homework question: The first numbetr is 4. A rule is multiply by 2 and then subtract 3. What are the first 6 numbers in the pattern
3 4 6 9 13 18...1....2....3....4......5
Subtract 2 from the previous number. 10-2 = 8 8-2 = 6 6-2 = 4 4-2 = 2
4*2-2=6 6*2-2=10
(n - 10) + 6
Keep subtracting 6
Homework question: The first numbetr is 4. A rule is multiply by 2 and then subtract 3. What are the first 6 numbers in the pattern
3 4 6 9 13 18...1....2....3....4......5
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
The rule of this pattern is -2 + 6 +4 so the next number would be 16.
5-30-6-42-7-56-8-72
add 6, subtract 2
There are several possible answers. One possibility is t(n) = (-n3 + 9n2 - 14n + 12)/6
3 4 5 6 The next number is 1 plus the previous number So the pattern rule is the next number is n + 1