IB Mathematics Analysis and Approaches Topic SL 1.3—geometric Sequences and Series Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 1.3—geometric Sequences and Series Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 1.3—geometric Sequences and Series with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.3—geometric Sequences and Series and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

A fund receives a single contribution of amount $C$ at the end of each year for $n$ years. Interest rate is $r > 0$ , compounded annually.

Show that the accumulated value after the $n$ th deposit is $C \frac{( 1 + r ) ^{n} - 1}{r}$ .

[3]

If instead $C$ is paid at the start of each year (annuity-due), show that the accumulated value after the $n$ th payment is $(1 + r) C \frac{( 1 + r ) ^{n} - 1}{r}$ .

[2]

A target amount $T$ (in the same currency as $C$ ) must be reached with an annuity-due. Find the least integer $n$ required.

[3]

Question 2

SL & HLPaper 2

Find the sum of the first six terms of the geometric progression $64, 48, 36, \dots$

[3]

Question 3

SLPaper 1

Consider a geometric sequence $(u_{n})$ with first term $a > 0$ and common ratio $0 < r < 1$ . Let $S_{n}$ be the sum of the first $n$ terms, and let $R_{n} = S_{\infty} - S_{n}$ .

Prove that $R_{n} = \frac{a r ^{n}}{1 - r}$ .

[3]

Suppose $S_{5} = \frac{31}{32} S_{\infty}$ . Find $r$ .

[3]

Question 4

SLPaper 2

Consider a geometric sequence with $u_{1} = \frac{18}{5}$ , $r > 0$ , and $u_2 u_3 u_4=\frac{729}{64}.$

Find $r$ .

[4]

Find the least value of $n$ such that $u_{n} < 1$ .

[4]

Question 5

SLPaper 1

A geometric sequence $(u_{n})$ has $u_{1} = \frac{9}{2}$ , $r > 0$ , and $u_2u_4u_6=\frac{1}{27}.$

Determine $r$ .

[4]

Hence find the least integer $n$ such that $u_{n} < \frac{1}{54}$ . Leave your answer in terms of logarithms.

[4]

IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

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IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 1.3—geometric Sequences and Series Questionbank

Unlock all 23 questions with a free account