IB Mathematics Applications & Interpretation Topic SL 1.3—geometric Sequences Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 1.3—geometric Sequences Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.3—geometric Sequences 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 mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

A student defines two sequences using the same positive number $y$ , where $y \neq = 1$ . The infinite geometric sequence has initial terms $4 lo g_{5} y, lo g_{5} y$ . The arithmetic sequence begins $lo g_{5} y, lo g_{5} (\frac{y}{25}), lo g_{5} (\frac{y}{625})$ . Let $S_{8}$ be the sum of the first 8 terms of the arithmetic sequence.

Determine the common ratio $r$ of the geometric sequence.

[2]

Demonstrate that the sum to infinity of this geometric sequence is $\frac{16}{3} lo g_{5} y$ .

[2]

Calculate the common difference $d$ of the arithmetic sequence as an integer value.

[4]

Verify that $S_{8} = 8 lo g_{5} y - 56$ .

[2]

If $S_{8}$ equals exactly three-fifths of the sum to infinity of the geometric sequence, solve for $y$ in the form $5^{p}$ , where $p \in Q$ .

[3]

Question 2

SLPaper 1

Consider an infinite geometric sequence $u_{n}$ with terms $5, - 15, 45, - 135, \dots$

Consider a second infinite geometric sequence $v_{n}$ with terms $5, 15, 45, 135, \dots$

A third sequence $w_{n}$ is defined as $w_{n} = u_{n} + v_{n}$ .

The finite series $\sum_{k = 1}^{122} w_{k}$ can be expressed in the form $\sum_{k = 0}^{N} 10 q^{k}$ .

Determine the first three non-zero terms of the sequence $w_{n}$ .

[3]

Find the common ratio $q$ .

[2]

Find the value of $N$ .

[2]

Question 3

HLPaper 1

For a geometric progression, the third term is $6$ and the sixth term is $\frac{2}{9}$ .

Determine the common ratio for this progression.

[3]

Calculate the sum to infinity for this specific progression.

[2]

Question 4

SLPaper 1

A clip's daily reposts form a geometric sequence. Day 5 has $48$ reposts and day 8 has $384$ .

Calculate the common ratio.

[2]

Determine the number of reposts on day 1.

[1]

Let $S_{k}$ be the total number of reposts in the first $k$ days. Determine the minimum integer value of $k$ such that $S_{k} > 6000$ .

[3]

Question 5

SLPaper 1

For a geometric sequence, the second term is $u_{2} = - 48$ and the fifth term is $u_{5} = 6$ . Determine the value of the first term in this sequence.

[5]

IB Mathematics Applications & Interpretation SL 1.3—geometric Sequences Questionbank

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IB Mathematics Applications & Interpretation SL 1.3—geometric Sequences Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 1.3—geometric Sequences Questionbank

Unlock all 31 questions with a free account