What is the sum of numbers lying between 107 and 253, which are divisible by 5 -

Options

A. 5220
B. 5210
C. 5200
D. 5000

Answer

To find the sum of numbers lying between 107 and 253 that are divisible by 5, we can follow these steps:

### Step 1: Identify the first and last terms
- The first number greater than 107 that is divisible by 5 is 110.
- The last number less than 253 that is divisible by 5 is 250.

### Step 2: Establish the arithmetic progression (AP)
- The numbers we are considering are: 110, 115, 120, ..., 250.
- This forms an arithmetic progression (AP) where:
- First term (a) = 110
- Common difference (d) = 5
- Last term (l) = 250

### Step 3: Find the number of terms (n) in the AP
To find the number of terms in the AP, we can use the formula for the nth term of an AP:
\[ l = a + (n - 1) \cdot d \]
Substituting the known values:
\[ 250 = 110 + (n - 1) \cdot 5 \]

### Step 4: Solve for n
Rearranging the equation:
\[ 250 - 110 = (n - 1) \cdot 5 \]
\[ 140 = (n - 1) \cdot 5 \]
Dividing both sides by 5:
\[ n - 1 = 28 \]
Thus,
\[ n = 29 \]

### Step 5: Calculate the sum of the AP
The sum \( S_n \) of the first n terms of an AP can be calculated using the formula:
\[ S_n = \frac{n}{2} \cdot (a + l) \]
Substituting the values we have:
\[ S_{29} = \frac{29}{2} \cdot (110 + 250) \]
\[ S_{29} = \frac{29}{2} \cdot 360 \]
\[ S_{29} = 29 \cdot 180 \]
\[ S_{29} = 5220 \]

### Conclusion
The sum of the numbers lying between 107 and 253 that are divisible by 5 is **5220**.

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