(x+1)+(x+4)+(x+7)+...+(x+28)=155 Cấp Số Cộng

Jasonbradley

2 min read

·

Jun 16, 2024

44

Share

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.