Well honey, there are 4 numbers in your combination, so it's as simple as 4 factorial, which is 4 x 3 x 2 x 1, giving you a total of 24 combinations using the numbers 1, 4, 6, and 9. That's all there is to it, no need to complicate things.
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To calculate the number of 4-number combinations using the numbers 1, 4, 6, and 9 without repetition, you can use the permutation formula. Since there are 4 options for the first number, 3 options for the second number, 2 options for the third number, and 1 option for the fourth number, you would multiply these numbers together: 4 x 3 x 2 x 1 = 24. Therefore, there are 24 different 4-number combinations using the numbers 1, 4, 6, and 9.
It is 917969.
1,469 multiplied by 4,675 is 6,867,575
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
There are an infinite number of possible answers - there are an infinite number of formulae that can be found to give t{1..5} = {12, 59, 294, 1469, 7344} which will give different values for t8. eg: t{n} = (376n⁴ - 3384n³ + 11186n² - 15369n + 7227)/3 gives t{1..5} = {12, 59, 294, 1469, 7344}, and t8 = 135889. t{n} = (-4929n⁵ + 76943n⁴ - 446037n³ +1198513n² -1473498n + 649296)/24 also gives t{1..5} = {12, 59, 294, 1469, 7344}, but t8 = -381656. However, the solution your teacher is probably expecting is based on the fact that: U1 = 12 U{n} = 5U{n-1} - 1 for n ≥ 2 This leads to: t1 = 12 t{n} = 12 + 47 × 5ⁿ⁻² for n ≥ 2 → t8 = 917969
You are multiplying by 5 and taking 1 away, so the next value is 36719.