Arithmetic and Geometric Sequences: Algebra 1 Math Test – PDF Download

Question 1: Identify the sequence (2 points)

Classify each sequence as arithmetic or geometric and give the next term.

1. \(12,19,26,33\) (1 point)
2. \(3,-6,12,-24\) (1 point)

Question 2: Arithmetic formula (2 points)

Consider the sequence \(9,5,1,-3\).

1. Write an explicit formula for \(a_{n}\). (1 point)
2. Find \(a_{12}\). (1 point)

Question 3: Geometric formula (2 points)

Consider the sequence \(7,14,28,56\).

1. Write an explicit formula for \(a_{n}\). (1 point)
2. Find \(a_{9}\). (1 point)

Question 4: Recursive formulas (2 points)

1. Write a recursive formula for the sequence \(100,85,70,55\). (1 point)
2. A sequence has \(a_{1}=2\) and \(a_{n}=5\cdot a_{n-1}\). Find \(a_{4}\). (1 point)

Question 5: Sequence from a table (3 points)

The table shows the first four terms of an arithmetic sequence.

1. Find the common difference. (1 point)
2. Write an explicit formula for \(a_{n}\). (1 point)
3. Which term of the sequence equals 140? (1 point)

Question 6: Sequence from a graph (3 points)

The graph shows the first four terms of a geometric sequence.

1. Find the common ratio. (1 point)
2. Write an explicit formula for \(a_{n}\). (1 point)
3. Find \(a_{7}\). (1 point)

Question 7: Arithmetic from two terms (2 points)

An arithmetic sequence has \(a_{4}=19\) and \(a_{9}=44\).

1. Find the common difference. (1 point)
2. Write an explicit formula for \(a_{n}\). (1 point)

Question 8: Geometric from two terms (2 points)

A geometric sequence has a positive common ratio, \(a_{2}=12\) and \(a_{4}=48\).

1. Find the common ratio. (1 point)
2. Find \(a_{6}\). (1 point)

Question 9: Growing plant (2 points)

Noah’s plant is 4 inches tall in week 1 and grows 1.5 inches each week. Let \(a_{n}\) be its height in week \(n\).

1. Write an explicit formula and find the height in week 9. (1 point)
2. In which week is the plant first taller than 30 inches? (1 point)

⬇ Download the Algebra 1 Arithmetic and Geometric Sequences test (PDF, 87 KB)

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