Find a formula for the $$ n $$ nh term in this arithmetic sequence: $$ a_{1}=28, a_{2}=21, a_{3}=14, a_{4}=7, \ldots $$ $$ a_{n}=[?] n+[] $$ Hint: The coefficient of $$ n $$ is the common difference.

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To find the formula for the $$ n $$-th term of the given arithmetic sequence:

$$ a_1 = 28, \ a_2 = 21, \ a_3 = 14, \ a_4 = 7, \ldots $$

**Step 1: Determine the Common Difference ($$ d $$)**

The common difference $$ d $$ in an arithmetic sequence is the difference between any two consecutive terms.

$$
d = a_2 - a_1 = 21 - 28 = -7
$$

**Step 2: Use the General Formula for an Arithmetic Sequence**

The general formula for the $$ n $$-th term of an arithmetic sequence is:

$$
a_n = a_1 + (n - 1)d
$$

Substituting the known values:

$$
a_n = 28 + (n - 1)(-7)
$$
$$
a_n = 28 - 7n + 7
$$
$$
a_n = -7n + 35
$$

**Final Formula:**

$$
a_n = -7n + 35
$$

**Verification:**

Let's verify the formula with the given terms:

- For $$ n = 1 $$:
  $$
  a_1 = -7(1) + 35 = 28
  $$
- For $$ n = 2 $$:
  $$
  a_2 = -7(2) + 35 = 21
  $$
- For $$ n = 3 $$:
  $$
  a_3 = -7(3) + 35 = 14
  $$
- For $$ n = 4 $$:
  $$
  a_4 = -7(4) + 35 = 7
  $$

All terms match the given sequence.

**Answer:**

After simplifying, the nth term is –7 · n plus 35. Thus,

aₙ = −7 n + 35
The nth term is –7 · n plus 35. Thus, $$ a_n = -7n + 35 $$

Find a formula for the \( n \) nh term in this arithmetic sequence: \( a_{1}=28, a_{2}=21, a_{3}=14, a_{4}=7, \ldots \) \[ a_{n}=[?] n+[] \] Hint: The coefficient of \( n \) is the common difference.

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