The sum of an arithmetic sequence is exactly 1150. The first term is 10, and the common difference increases by 5 each term. After how many terms is the total sum 1150?

Sun, 19 Apr 2026 22:57:36 +0000

**Why Are More People Solving “Sum of an Arithmetic Sequence Is Exactly 1150 With First Term 10 and Increasing Difference?”**
*The sum of an arithmetic sequence is exactly 1150. The first term is 10, and the common difference increases by 5 each term. After how many terms is the total sum 1150?* In a digital landscape growing more analytical and curious by the day, a growing number of users are exploring patterns hidden in everyday math—like how a sequence grows without a clear pattern. This particular problem draws attention because it blends foundational math with a subtle twist: the common difference isn’t constant, making it more engaging than a standard arithmetic problem. People are naturally curious when numbers tell a story shaped by change, not just steady steps—mirroring real-world trends where growth shifts unpredictably. This sequence begins at 10, and each next term increases by 5 more than the last: 10, then 10 + (5), then 10 + (5+5), etc. The challenge lies in determining exactly how many such adjusted steps are needed so the cumulative total reaches 1150. **How It Actually Works**
To solve for the number of terms when the total sum equals 1150, start by defining the sequence formally:
- First term: $ a = 10 $
- Difference increases by 5 each term: $ d_1 = 5, d_2 = 10, d_3 = 15, \ldots $