Precalculus Sequences and Series Test Solutions and Scoring (PDF)

Precalculus math test solutions: Sequences and Series – Maths PDF

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This precalculus sequences series test answers 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.

Worked solutions and scoring notes for the 9-question sequences and series test. Use the scoring line under each solution to award partial credit.

Precalculus · Common Core State Standards: F-IF.A.3, F-BF.A.2, A-SSE.B.4

Precalculus sequences series test answers: worked solutions

Question 1 – Arithmetic terms [2 pts]

\(-2,3,8,13\). \(a_{15}=-2+5(14)=68\).

\(-2,3,8,13\); \(a_{15}=68\)

Scoring: 1 point for the terms, 1 point for a15.

Question 2 – Geometric term [2 pts]

\(a_{6}=5(-2)^{5}=5(-32)\).

\(-160\)

Scoring: 1 point for the formula, 1 point for the value.

Question 3 – Recursive to explicit [2 pts]

Arithmetic with \(d=-3\): \(a_{n}=7-3(n-1)=10-3n\).

\(a_{n}=10-3n\)

Scoring: 1 point for d, 1 point for the formula.

Question 4 – Arithmetic sum [2 pts]

\(a_{25}=4+24(3)=76\). \(S_{25}=\frac{25}{2}(4+76)=1000\).

1000

Scoring: 1 point for a25, 1 point for the sum.

Question 5 – Read a sequence graph [3 pts]

Ratio 2.

(a) \(\frac{6}{3}=\frac{12}{6}=2\). (b) \(a_{n}=3\cdot2^{n-1}\). (c) \(3\cdot2^{7}=384\).

\(2\); \(a_{n}=3\cdot2^{n-1}\); \(384\)

Scoring: 1 point for each part.

Question 6 – Sigma notation [2 pts]

\(a_{1}=4\), \(r=\frac12\), \(n=5\). \(S_{5}=4\cdot\frac{1-\frac{1}{32}}{\frac12}=8\cdot\frac{31}{32}=\frac{31}{4}\).

\(\frac{31}{4}=7.75\)

Scoring: 1 point for the setup, 1 point for the value.

Question 7 – Infinite series [2 pts]

\(|r|< 1\). \(S=\frac{12}{1-\frac13}=\frac{12}{2/3}=18\).

Scoring: 1 point for checking |r| < 1, 1 point for the sum.

Question 8 – Bouncing ball [3 pts]

Rebound heights 15, 11.25, 8.4375.

(a) \(20(0.75)^{3}=8.4375\) ft. (b) Up-heights: \(\frac{15}{1-0.75}=60\). Total \(=20+2(60)=140\) ft.

\(8.4375\) ft; \(140\) ft

Scoring: 1 point for (a), 2 points for (b).

Question 9 – Repeating decimal [2 pts]

\(0.27+0.0027+\text{ … }\): \(a_{1}=0.27\), \(r=0.01\). \(S=\frac{0.27}{0.99}=\frac{27}{99}=\frac{3}{11}\).

\(\frac{3}{11}\)

Scoring: 1 point for the series, 1 point for the fraction.

Total score

Total

20 points

Key facts behind this precalculus sequences series test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Precalculus chapters: Precalculus math.

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