Algebra 2 Arithmetic and Geometric Sequences and Series Test with Point Values (PDF)

Algebra 2 math test: Arithmetic and Geometric Sequences and Series – Maths PDF

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This algebra 2 sequences series test for Algebra 2 covers arithmetic and geometric sequences and series (Common Core F-BF.A.2, A-SSE.B.4, F-IF.A.3), with a free PDF to print.

This 45-minute test on arithmetic and geometric sequences and series has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Arithmetic and Geometric Sequences and Series
Standards: F-BF.A.2, A-SSE.B.4, F-IF.A.3
Time: 45 minutes
Total: 20 points

Algebra 2 sequences series test: questions

Question 1 – List the terms [2 pts]

Write the first four terms of \(a_{n} = 2n^{2} – 3\).

Question 2 – Arithmetic formula [3 pts]

First five terms of an arithmetic sequence.

The graph shows the first five terms of an arithmetic sequence. Write an explicit formula and find \(a_{30}\).

Question 3 – Geometric formula [2 pts]

Write an explicit formula for \(5, 15, 45, …\) and find \(a_{6}\).

Question 4 – Arithmetic series [3 pts]

Find the sum of the first 25 terms of the arithmetic sequence \(a_{n} = 4n – 1\).

Question 5 – Geometric series [3 pts]

Find the sum of the first 6 terms of \(2 + 6 + 18 + …\).

Question 6 – Recursive formula [2 pts]

Write a recursive formula for \(48, 24, 12, 6, …\) and find the next two terms.

Question 7 – Stadium seating [2 pts]

A stack of logs with 4 in the bottom row.

A section has 8 seats in the first row and each row has 3 more seats than the previous row. There are 12 rows. How many seats are in the section? (The picture shows a triangular stack for comparison.)

Question 8 – Identify the type [2 pts]

Terms of a sequence.

Is the sequence in the table arithmetic or geometric? Write an explicit formula and find \(a_{7}\).

Question 9 – Find the error [1 pt]

Jamal used \(S_{n} = \frac{n(a_{1} + a_{n})}{2}\) for \(1 + 2 + 4 + 8 + 16\) and got 40. Explain the error.

Key facts behind this algebra 2 sequences series test

Key facts

A sequence is a function whose domain is the positive integers.
Arithmetic: a_n = a_1 + (n – 1)d; geometric: a_n = a_1·r^(n-1).
Recursive formulas build each term from the previous one.
Arithmetic sum: S_n = n(a_1 + a_n)/2.
Geometric sum: S_n = a_1(1 – r^n)/(1 – r), r ≠ 1.

How to use this algebra 2 sequences series test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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