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Home » Use the principle of inclusion-exclusion on adjacency pairs** — but that’s too vast. - RTA

Use the principle of inclusion-exclusion on adjacency pairs** — but that’s too vast. - RTA

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 Since the middle term is given as 2, we have \(a = 2\).

📌 So the terms are:

📌 -4, \quad -1, \quad 2, \quad 5, \quad 8

📌 Now compute the sum of the squares:

📌 This matches the given sum. Therefore, the first term is \(\boxed{-4}\).**Question:** A palynologist is analyzing pollen concentration data and models the relationship using a quadratic function. If the pollen concentration \( P(x) \) over time \( x \) is given by \( P(x) = ax^2 + bx + c \), and it's known that \( P(1) = 6 \), \( P(2) = 11 \), and \( P(3) = 18 \), determine the values of \( a \), \( b \), and \( c \).

📌 Solution:** We are given the quadratic function \( P(x) = ax^2 + bx + c \) and the points \( P(1) = 6 \), \( P(2) = 11 \), and \( P(3) = 18 \). We can set up the following system of equations by substituting the known values:

📌 \( a(1)^2 + b(1) + c = 6 \) which simplifies to \( a + b + c = 6 \).

📌 \( a(2)^2 + b(2) + c = 11 \) which simplifies to \( 4a + 2b + c = 11 \).

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