Precalculus Sequences and Series Test with Point Values (PDF)

Precalculus math test: Sequences and Series – Maths PDF

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

This 20-point test covers arithmetic and geometric sequences, sigma notation, finite and infinite sums and a bouncing-ball model (F-IF.A.3, F-BF.A.2, A-SSE.B.4). You have 45 minutes. Show your work.

Time and points

About this test

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

Precalculus sequences series test: questions

Question 1 – Arithmetic terms [2 pts]

The first four terms.

For \(a_{n}=-2+5(n-1)\), list the first four terms and find \(a_{15}\).

Question 2 – Geometric term [2 pts]

A geometric sequence has \(a_{1}=5\) and \(r=-2\). Find \(a_{6}\).

Question 3 – Recursive to explicit [2 pts]

A sequence has \(a_{1}=7\) and \(a_{n}=a_{n-1}-3\). Write an explicit formula.

Question 4 – Arithmetic sum [2 pts]

Find the sum of the first \(25\) terms of \(4,7,10,\text{ … }\).

Question 5 – Read a sequence graph [3 pts]

A sequence graph.

The graph shows the first four terms of a geometric sequence. (a) Find the common ratio. (b) Write \(a_{n}\). (c) Find \(a_{8}\).

Question 6 – Sigma notation [2 pts]

Evaluate \(\sum_{k=1}^{5}4\left(\frac12\right)^{k-1}\).

Question 7 – Infinite series [2 pts]

Find the sum of the infinite series with \(a_{1}=12\) and \(r=\frac13\).

Question 8 – Bouncing ball [3 pts]

A ball dropped from 20 feet.

A ball is dropped from \(20\) ft and rebounds to \(75\%\) of its previous height each time. (a) How high is the third rebound? (b) Find the total distance traveled before it stops.

Question 9 – Repeating decimal [2 pts]

Write \(0.\overline{27}\) as a fraction using an infinite series.

Key facts behind this precalculus sequences series test

Key facts

Arithmetic: a_n = a_1 + (n – 1)d; sum S_n = (n/2)(a_1 + a_n).
Geometric: a_n = a_1 r^(n-1); sum S_n = a_1(1 – r^n)/(1 – r).
Sigma notation adds the terms from the lower index to the upper index.
An infinite geometric series converges only if |r| < 1, and then S = a_1/(1 - r).
A recursive formula gives each term from the one before it.

How to use this precalculus 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 Precalculus chapters: Precalculus math.

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