- **Finding the Common Difference**
To find the common difference of the AP, we need to consider that the terms leave a remainder of 3 when divided by 4. This means the terms can be represented as 4n + 3, where n is a natural number.
- **Finding the First Term**
To find the first term of the AP, we need to consider that the first term leaves a remainder of 3 when divided by 4. Therefore, the first term can be represented as 4(1) + 3 = 7.
- **Sum of the 30 Terms**
The sum of the first n terms of an AP can be calculated using the formula: Sn = n/2 [2a + (n-1)d], where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
- **Calculating the Sum**
In this case, n = 30, a = 7, and we have already found the common difference to be 4. Substituting these values into the formula, we get: S30 = 30/2 [2(7) + (30-1)4] = 15 [14 + 116] = 15 * 130 = 1950.
- **Conclusion**
Therefore, the sum of the 30 terms of the AP whose terms leave a remainder of 3 when divided by 4 is 1950.