Determine the Term-to-Term Rule for the Sequence: 13, 10, 7, 4

To identify the term-to-term rule of the sequence $13, 10, 7, 4, \ldots$, let's analyze the differences between consecutive terms:

• From 13 to 10: $10 - 13 = -3$
• From 10 to 7: $7 - 10 = -3$
• From 7 to 4: $4 - 7 = -3$

The common difference is $-3$, confirming the sequence is arithmetic. In an arithmetic sequence, we use the formula $a_n = a_1 + (n-1) \times d$.

Here, $a_1 = 13$, and the common difference $d = -3$. Plug these into the formula:

$a_n = 13 + (n-1)(-3)$

Simplify the expression:

$a_n = 13 - 3(n-1)$

$a_n = 13 - 3n + 3$

$a_n = 16 - 3n$

Thus, the term-to-term rule of the sequence is $16-3n$. This matches choice 3 from the provided options.