Multiplies by 3, then subtracts 7
The simplest is Un = 2n + 1
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
3 4 6 9 13 18...1....2....3....4......5
t(n) = 5 + 2*n
The pattern rule is: 4 5 6 7 8 and so the next number will be 33+9 = 42
The rule for the pattern is y=x+2. That rule is in the table format in which it would originally be in, but the worded rule would be 'It increases by 2 each time'.
+2, +3, +2
Reducing squares 9 x 9 = 81 8 x 8 = 64 7 x 7 = 49 6 x 6 = 36 so next would be 5 x 5 = 25
Multiplies by 3, then subtracts 7
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The simplest is Un = 2n + 1
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
The rule of this pattern is obfuscated by the omission of spaces, giving the impression that this is the number "111,359,173,157". However, the underlying pattern follows the function of the Fibonacci series, but adding sets of 3 instead of sets of 2. So, 1+1+1=3, 1+1+3=5, 1+3+5=9, 3+5+9=17, 5+9+17=31, 9+17+31=57.
3 4 6 9 13 18...1....2....3....4......5
Unfortunately, the third set could be any numeral(s) at all. To simplify the analysis, look at the following elementary question: Given the series 3, 5, 7, 9 what are the next two numbers? Many people will suggest 11, 13. But the fact is that the problem does not rule out or rule in any series from which the sample 3, 5, 7, 9 could have been taken. Of course, the series could be odd ordinal integers: 3, 5, 7, 9, 11, 13 etc. But it could also be 3, 5, 7, 9, 7, 5, 3, 5, 7, 9, 7.... or 3, 5, 7, 9, 9, 9, 9, 9.... or 1, 3, 5, 7, 9, 2, 3, 5, 7, 9, 3, 3, 5, 7, 9, 4, 3, 5, 7, 9....Or any series at all! Problems of this kind require that we make assumptions about the relationships between the numbers. If the test is whether we will make the same assumptions that intelligent people usually make, then there might be a unique solution to the problem. But if there are no stated restraints on the assumptions, then there is no unique solution.
t(n) = 5 + 2*n