11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
D
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
75
217
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
D
JSUN
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
M and N
2
122
12
75
2310.
16384
1