Determine the number of multiples of 4 that lie between 10 and 250.

Answer

To determine the number of multiples of 4 that lie between 10 and 250, we can follow these steps:

### Step 1: Identify the first multiple of 4 greater than 10
The first multiple of 4 after 10 is 12. (4 x 3 = 12)

### Step 2: Identify the last multiple of 4 less than or equal to 250
The last multiple of 4 before 250 is 248. (4 x 62 = 248)

### Step 3: Write the sequence of multiples of 4
The multiples of 4 between 10 and 250 can be represented as:
12, 16, 20, ..., 248.

### Step 4: Identify the first term (A), common difference (D), and last term (An)
- First term (A) = 12
- Common difference (D) = 4 (since we are counting multiples of 4)
- Last term (An) = 248

### Step 5: Use the formula for the nth term of an arithmetic sequence
The formula for the nth term of an arithmetic sequence is given by:
\[ An = A + (N - 1) \cdot D \]

### Step 6: Substitute the known values into the formula
Substituting the known values:
\[ 248 = 12 + (N - 1) \cdot 4 \]

### Step 7: Solve for N
1. Rearranging the equation:
\[ 248 - 12 = (N - 1) \cdot 4 \]
\[ 236 = (N - 1) \cdot 4 \]

2. Dividing both sides by 4:
\[ N - 1 = \frac{236}{4} \]
\[ N - 1 = 59 \]

3. Adding 1 to both sides:
\[ N = 59 + 1 \]
\[ N = 60 \]

### Conclusion
The number of multiples of 4 that lie between 10 and 250 is **60**.

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