5Question: A palynologist analyzes five pollen samples with counts forming an arithmetic sequence. The sum of the first and fifth counts is 120, and the product of the second and fourth counts is 1452. Find the third count.

Mon, 04 May 2026 17:59:51 +0000

**5Question: A palynologist analyzes five pollen samples with counts forming an arithmetic sequence. The sum of the first and fifth counts is 120, and the product of the second and fourth counts is 1452. Find the third count.** Why is a simple arithmetic sequence in pollen counts suddenly generating interest? In fields like palynology—the study of pollen and spores—looking beyond visible patterns reveals hidden trends in climate, ecology, and agriculture. This question involves precisely that: a mathematical breakdown built around ten pollen grain counts arranged in a clear sequence. Each value follows a steady rhythm, making it ideal for testing assumptions about symmetry and relationships in nature’s data. The challenge isn’t just in computing numbers—it’s in understanding how patterns mirror real-world environmental shifts. This problem is gaining momentum due to growing attention in environmental science and data-driven research. With rising focus on pollen trends as climate indicators, simple yet precise mathematical modeling offers fresh insight into environmental monitoring and biodiversity analysis. The structured sequence—first to fifth—creates a natural balance, where the outer values (first and fifth) average to 120, while inner values (second and fourth) multiply to 1452. Solving this connects raw numbers to meaningful biological interpretation. Let’s unpack the math. In an arithmetic sequence, each term increases by a constant difference. Let the five counts be expressed as:
**a, a + d, a + 2d, a + 3d, a + 4d**
where *a* is the first term and *d* is the common difference.