Which of the following is not an accurate formula to describe the following arithmetic sequence? $$ \begin{array}{l}78,72,66,60,54 \ldots \ a_{n}=-6 n+90 \ a_{n}=78-6(n-1) \ a_{n}=84-6 n \ a_{n}=-6 n+84\end{array} $$

Question

UpStudy AI · Accepted Answer

Let's analyze each formula to determine which one does **not** accurately describe the arithmetic sequence $$78, 72, 66, 60, 54, \ldots$$.

### Given:
- **First Term ($$a_1$$)**: 78
- **Common Difference ($$d$$)**: $$-6$$

The general formula for the $$n$$-th term of an arithmetic sequence is:
$$ a_n = a_1 + (n-1)d $$
Substituting the known values:
$$ a_n = 78 + (n-1)(-6) = 78 - 6(n-1) $$

### Evaluating Each Option:

1. **$$a_n = -6n + 90$$**
   - **For $$n = 1$$:** 
     $$ a_1 = -6(1) + 90 = 84 $$
     - **Expected:** 78
     - **Result:** **Incorrect**

2. **$$a_n = 78 - 6(n-1)$$**
   - **For $$n = 1$$:** 
     $$ a_1 = 78 - 6(0) = 78 $$
   - **For $$n = 2$$:** 
     $$ a_2 = 78 - 6(1) = 72 $$
     - **Result:** **Correct**

3. **$$a_n = 84 - 6n$$**
   - **For $$n = 1$$:**
     $$ a_1 = 84 - 6(1) = 78 $$
   - **For $$n = 2$$:**
     $$ a_2 = 84 - 6(2) = 72 $$
     - **Result:** **Correct**

4. **$$a_n = -6n + 84$$**
   - This is algebraically equivalent to the third option and will yield the same results.
     - **Result:** **Correct**

### Conclusion:
Only the first formula **does not** accurately describe the given arithmetic sequence.

**Answer:**  
$$a_{n}=-6 n+90$$ is not an accurate formula for the given sequence.
$$a_{n}=-6 n+90$$ is not an accurate formula for the given sequence.

Which of the following is not an accurate formula to describe the following arithmetic
sequence?

Upstudy AI Solution

Answer

Solution

Given:

Evaluating Each Option:

Conclusion:

The Deep Dive

Related Questions

Latest Pre Algebra Questions