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The third and fifth terms of an arithmetic sequence are 2 and 32 , respectively. Find explicit and recursive formulas for the sequence

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\boxed{a_n=a_1+(n-1)d}


2=a_1+(3-1)d\\32=a_1+(5-1)d\\\\a_1+2d=2\\a_1+4d=32

Subtracting the first equation from the second, we get


2d=30\\d=15


a_1+30=2\\a_1=-28

Therefore, the explicit formula is


a_n=-28+(n-1)\cdot15\\a_n=-28+15n-15\\a_n=15n-43

The recursive formula is


a_1=-28\\a_n=a_(n-1)+15

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