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Instructions: Given the recursive rule, match it to the explicit form.Recursive: an=anโˆ’1+9๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+9a1=13๐‘Ž1=13Drag answer hereRecursive: an=anโˆ’1+4๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+4a1=โˆ’22๐‘Ž1=โˆ’22Drag answer hereRecursive: an=anโˆ’1โˆ’9๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’9a1=3๐‘Ž1=3Drag answer hereRecursive: an=anโˆ’1+20๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+20a1=โˆ’38๐‘Ž1=โˆ’38Drag answer hereExplicit: an=12โˆ’9n๐‘Ž๐‘›=12โˆ’9๐‘›Explicit: an=4+9n๐‘Ž๐‘›=4+9๐‘›Explicit: an=โˆ’26+4n๐‘Ž๐‘›=โˆ’26+4๐‘›Explicit: an=โˆ’58+20n๐‘Ž๐‘›=โˆ’58+20๐‘›

Question

Instructions: Given the recursive rule, match it to the explicit form.Recursive: an=anโˆ’1+9๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+9a1=13๐‘Ž1=13Drag answer hereRecursive: an=anโˆ’1+4๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+4a1=โˆ’22๐‘Ž1=โˆ’22Drag answer hereRecursive: an=anโˆ’1โˆ’9๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’9a1=3๐‘Ž1=3Drag answer hereRecursive: an=anโˆ’1+20๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1+20a1=โˆ’38๐‘Ž1=โˆ’38Drag answer hereExplicit: an=12โˆ’9n๐‘Ž๐‘›=12โˆ’9๐‘›Explicit: an=4+9n๐‘Ž๐‘›=4+9๐‘›Explicit: an=โˆ’26+4n๐‘Ž๐‘›=โˆ’26+4๐‘›Explicit: an=โˆ’58+20n๐‘Ž๐‘›=โˆ’58+20๐‘›

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Solution

The recursive and explicit forms can be matched as follows:

  1. Recursive: an = anโˆ’1 + 9, a1 = 13 matches with Explicit: an = 4 + 9n. This is because the recursive rule adds 9 to the previous term, and the explicit rule also adds 9 for each term (n).

  2. Recursive: an = anโˆ’1 + 4, a1 = -22 matches with Explicit: an = -26 + 4n. This is because the recursive rule adds 4 to the previous term, and the explicit rule also adds 4 for each term (n).

  3. Recursive: an = anโˆ’1 - 9, a1 = 3 matches with Explicit: an = 12 - 9n. This is because the recursive rule subtracts 9 from the previous term, and the explicit rule also subtracts 9 for each term (n).

  4. Recursive: an = anโˆ’1 + 20, a1 = -38 matches with Explicit: an = -58 + 20n. This is because the recursive rule adds 20 to the previous term, and the explicit rule also adds 20 for each term (n).

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