The seventh number is a sequence of numbers is 31 and each number after the first number in the sequence is 4 less than the number immediately preceding it. What is the fourth number in the sequece?

Options

A. 15
B. 19
C. 35
D. 43

Answer

To solve the problem step by step, we will use the information provided about the sequence.

### Step 1: Understand the Given Information
We know that the 7th term of the sequence (a7) is 31. Each subsequent number in the sequence is 4 less than the number immediately preceding it. This indicates that the sequence is an arithmetic sequence with a common difference (d) of -4.

### Step 2: Write the General Formula for the nth Term
The general formula for the nth term of an arithmetic sequence is given by:
\[ a_n = a_1 + (n - 1) \cdot d \]
where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step 3: Substitute Known Values for the 7th Term
We know:
- \( a_7 = 31 \)
- \( d = -4 \)

Substituting these values into the formula for the 7th term:
\[ 31 = a_1 + (7 - 1)(-4) \]
This simplifies to:
\[ 31 = a_1 + 6 \cdot (-4) \]
\[ 31 = a_1 - 24 \]

### Step 4: Solve for the First Term (a1)
Now, we can solve for \( a_1 \):
\[ a_1 = 31 + 24 \]
\[ a_1 = 55 \]

### Step 5: Find the Fourth Term (a4)
Now that we have \( a_1 \), we can find the fourth term \( a_4 \) using the same formula:
\[ a_4 = a_1 + (4 - 1)(-4) \]
Substituting \( a_1 = 55 \):
\[ a_4 = 55 + 3 \cdot (-4) \]
\[ a_4 = 55 - 12 \]
\[ a_4 = 43 \]

### Conclusion
The fourth number in the sequence is **43**.

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