## Solving the Arithmetic Series: (x+1)+(x+4)+(x+7)+...+(x+28)=155

This problem presents an arithmetic series where we need to find the value of 'x'. Let's break down the steps to solve it:

### Understanding Arithmetic Series

An arithmetic series is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference.

In this series:

**First Term (a):**x+1**Common Difference (d):**3 (notice the difference between consecutive terms is 3)**Last Term (l):**x+28**Sum (S):**155

### Using the Formula for Sum of Arithmetic Series

The formula for the sum (S) of an arithmetic series is:

**S = (n/2) * [2a + (n-1)d]**

Where:

**n:**Number of terms in the series

**1. Find the number of terms (n):**

- The series starts at (x+1) and ends at (x+28).
- The difference between consecutive terms is 3.
- Therefore, the number of terms (n) is: (28-1)/3 + 1 = 10

**2. Substitute the values into the formula:**

- S = 155
- n = 10
- a = x+1
- d = 3

**155 = (10/2) * [2(x+1) + (10-1)3]**

**3. Solve for 'x':**

- 155 = 5 * [2x + 2 + 27]
- 155 = 5 * [2x + 29]
- 155 = 10x + 145
- 10x = 10
**x = 1**

### Conclusion

Therefore, the value of **x** in the arithmetic series (x+1)+(x+4)+(x+7)+...+(x+28)=155 is **1**.