There are infinitely polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest rule, based on a polynomial of order 4 is
T(n) = (n^4 - 12n^3 + 50n^2 - 78n + 42)/3 for n = 1, 2, 3, ...
8. Each number is the sum of the previous two.
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
Add the previous 2 numbers to get the next number.
3 4 5 6 The next number is 1 plus the previous number So the pattern rule is the next number is n + 1
for 3: count all number if divisable by 3 (123= 1+2+3= 6, 3+3=6) for 5:end number is 5 or 0
8. Each number is the sum of the previous two.
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
Add the previous 2 numbers to get the next number.
3 4 5 6 The next number is 1 plus the previous number So the pattern rule is the next number is n + 1
Any number that ends in zero is divisible by 10, 5, 2 and 1.
for 3: count all number if divisable by 3 (123= 1+2+3= 6, 3+3=6) for 5:end number is 5 or 0
The rule of the Fibonacci sequence is simple. Take the previous number in the sequence, and add it to the current number. The sequence starts with 0 and 1. 0, 1 So, add 0+1=1. The sequence now contains three numbers. 0, 1, 1 Now, add 1+1=2. This brings us to four numbers. 0, 1, 1, 2 Add 1 and 2. (1+2=3) 0, 1, 1, 2, 3 Now it gets a bit tricky. Add 2+3=5, so the next number is 5. 0, 1, 1, 2, 3, 5 Continue to add the numbers accordingly. (3+5=8) 0, 1, 1, 2, 3, 5, 8 Proceed. 0, 1, 1, 2, 3, 5, 8, 13, 25, 38, 63, 101, 164...
If the rules for 2 and 3 work, the number is divisibale by 5.
The gaps are 5, 10, 15, 20, ..... The rule becomes add 5(n-1) to the previous number So that the second number is found by adding 5 times (2-1) to 1 = 5+1 = 6 and the third number is found by adding 5 times (3-1) to 6 = 10+6 = 16 and the fourth number is found by adding 5 times (4-1) to 16 = 15+15 = 31 and so on....
the rule is mutltiply by 3 and add 2... hope that helps.
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
A mix number is one whole number and a fraction, there for the numbers 1 2 5 can be come the mixed number 1 2/5.