Question

Write the explicit rule of the sequence -1/3, -1 2/3, -3, -4 1/3. How would you do this?

Answer 1

The explicit rule of the sequence is
`\( a_n = -(1)/(3) - (n-1)/(3) \)`, where
`\( n \)`is the term number.

Step-by-step explanation:

The sequence given is an arithmetic sequence, where each term is obtained by subtracting a common difference from the previous term. In this case, the common difference is
`\(-(4)/(3)\)`. To find the explicit rule for the sequence, we can use the formula for the
`\(n\)-th` term of an arithmetic sequence:
`\(a_n = a_1 + (n-1)d\)`, where
`\(a_n\)` is the
`\(n\)-th` term,
`\(a_1\)` is the first term,
`\(n\)` is the term number, and
`\(d\)` is the common difference.

Given the first term
`\(a_1 = -(1)/(3)\)` and the common difference
`\(d = -(4)/(3)\)`, we substitute these values into the formula to get
`\(a_n = -(1)/(3) - (n-1)/(3)\)` as the explicit rule for the sequence.

This formula allows us to find any term in the sequence by plugging in the corresponding term number
`\(n\)`. The negative sign in front of
`\((1)/(3)\)`indicates that each term is decreasing, and the magnitude of the decrease is
`\((1)/(3)\)` for each term.