The first six numbers in a pattern are listed below. $$ -19.2-18.4 \quad-17.6 \quad-16.8 \quad-16 \quad-15.2 $$ Write an expression that could be used to determine the 100 th number in the pattern. You must show work.

Question

UpStudy AI · Accepted Answer

To determine the 100th number in the given pattern, we'll analyze the sequence and derive an appropriate expression.

### Given Sequence:
$$
-19.2, \quad -18.4, \quad -17.6, \quad -16.8, \quad -16, \quad -15.2
$$

### Step 1: Identify the Pattern Type
The sequence appears to be **arithmetic**, where each term increases by a constant difference.

### Step 2: Determine the Common Difference ($$d$$)
Calculate the difference between consecutive terms:
$$
d = -18.4 - (-19.2) = 0.8
$$
$$
d = -17.6 - (-18.4) = 0.8
$$
$$
\vdots
$$
The common difference $$d = 0.8$$ for all consecutive terms.

### Step 3: Find the First Term ($$a_1$$)
$$
a_1 = -19.2
$$

### Step 4: Derive the General Formula for the $$n$$-th Term
For an arithmetic sequence, the $$n$$-th term ($$a_n$$) is given by:
$$
a_n = a_1 + (n - 1) \times d
$$
Substituting the known values:
$$
a_n = -19.2 + (n - 1) \times 0.8
$$

### Step 5: Calculate the 100th Term ($$a_{100}$$)
$$
a_{100} = -19.2 + (100 - 1) \times 0.8
$$
$$
a_{100} = -19.2 + 99 \times 0.8
$$
$$
a_{100} = -19.2 + 79.2
$$
$$
a_{100} = 60
$$

### Final Expression
The expression to determine the 100th number in the pattern is:
$$
a_{100} = -19.2 + 99 \times 0.8
$$

Alternatively, the general expression for the $$n$$-th term is:
$$
a_n = -19.2 + (n - 1) \times 0.8
$$
The 100th number in the pattern is 60.

The first six numbers in a pattern are listed below.

Write an expression that could be used to determine the 100 th number in the pattern. You must show work.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Pre Algebra Questions

The first six numbers in a pattern are listed below. Write an expression that could be used to determine the 100 th number in the pattern. You must show work.