Question

Write the recursive rule and the iterative rule for the following sequence: 10, 6, 2, -2, -6

Answer 1

The recursive rule is

`a_n=a_(n-1)+(-4)`.
The iterative rule is

`a_n=14-4n`

The recursive rule is given by the formula

`a_n=a_(n-1)+d`, where d is the common difference. Our common difference is -4, which gives us the recursive rule above.

The iterative rule begins with the formula

`a_n=a_1+d(n-1)`, where a₁ is the first term and d is the common difference. Our first term is 10 and our common difference is -4:

`a_n=10+(-4)(n-1) \\\text{Using the Distributive Property,} \\ \\a_n=10+(-4*n)+(-4*-1) \\ \\a_n=10-4n+4 \\ \\\text{Combining like terms,} \\ \\a_n=14-4n`