Finding the Common Difference and nth Term
Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-
Step-by-step video solution
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Problem and lesson overview
Question:
A swimming pool's water level is being monitored daily. On day 1, the level is 48 inches. On day 2, it is 46 inches. On day 3, it is 44 inches. Identify the common difference and write an explicit formula for the water level after n days. Then find the water level on day 12.
Finding the Common Difference and nth Term
This lesson walks through identifying the common difference of an arithmetic sequence, building an explicit formula of the form , and using that formula to find any term. A real-world decreasing sequence is used to connect arithmetic sequences to linear functions.
In this lesson, you will learn to:
• Identify the common difference of an arithmetic sequence by subtracting consecutive terms.
• Write an explicit formula for an arithmetic sequence using the formula .
• Simplify and verify an explicit formula against known
A swimming pool's water level is being monitored daily. On day 1, the level is 48 inches. On day 2, it is 46 inches. On day 3, it is 44 inches. Identify the common difference and write an explicit formula for the water level after n days. Then find the water level on day 12.
Finding the Common Difference and nth Term
This lesson walks through identifying the common difference of an arithmetic sequence, building an explicit formula of the form , and using that formula to find any term. A real-world decreasing sequence is used to connect arithmetic sequences to linear functions.
In this lesson, you will learn to:
• Identify the common difference of an arithmetic sequence by subtracting consecutive terms.
• Write an explicit formula for an arithmetic sequence using the formula .
• Simplify and verify an explicit formula against known
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