Question

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

Answer 1

`\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`