Recursive and Explicit Formulas in Real-World Context

Question:
A concert venue adds seats in arithmetic sequence rows. Row 8 has 72 seats and row 12 has 88 seats. Write both a recursive formula — a of n equals a of n minus 1, plus d — and an explicit formula — a of n equals a of 1, plus the quantity n minus 1 times d — for the number of seats in row n. Then find the total number of seats in the first 15 rows.

Recursive and Explicit Formulas in Real-World Context

This lesson connects arithmetic sequences to linear functions by finding recursive and explicit formulas from two known terms. Students apply the arithmetic series sum formula to find a total, reinforcing the relationship between sequences, slope, and linear equations.

In this lesson, you will learn to:
• Find the common difference of an arithmetic sequence from two non-consecutive terms
• Write both recursive and explicit formulas for an arithmetic sequence
• Verify a formula u