IB Mathematics Applications & Interpretation Topic SL 1.2—sequences and Sigma Notation Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 1.2—sequences and Sigma Notation Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.2—sequences and Sigma Notation with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.2—sequences and Sigma Notation and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

An arithmetic sequence has first term 14 and second term 9.

Determine the common difference.

[2]

Calculate the 12th term of the sequence.

[2]

Work out the total sum of the first twelve terms.

[2]

Question 2

SLPaper 2

A vineyard plants vines in rows so that each new row contains a fixed number more vines than the previous row. In one section, row 1 has 24 vines and row 17 has 88 vines, so the numbers of vines per row form an arithmetic sequence. Let $v_{n}$ be the number of vines in row $n$ , and let $T_{n}$ be the total number of vines in the first $n$ rows.

Find the common difference.

[3]

Write an expression for $v_{n}$ .

[3]

Find the total number of vines in the first 17 rows.

[3]

Show that $T_{n} = \frac{n}{2} (4 n + 44)$ .

[4]

Find the number of vines in row 30.

[3]

Find the number of rows in the section if the section contains 1680 vines in total.

[4]

A second section has 21 rows. The first row has 18 vines and the total number of vines is 1008. Find the number of vines in the last row.

[4]

Using your answer to the previous part, find the common difference for the second section.

[3]

Question 3

HLPaper 2

An arithmetic progression has terms $v_{1} = 1.8$ , $v_{2} = 2.1$ , and a specific term $v_{k} = 64.8$ . Consider the terms $v_{n}$ where $n \leq k$ . Let $R$ be the total sum of all terms $v_{n}$ for which $n$ is not a multiple of $4$ .

Calculate the value of $k$ .

[4]

Determine the total sum of the sequence from $n = 1$ to $k$ .

[2]

Show that $R = 5294.7$ .

[5]

An infinite geometric sequence has sum to infinity $S_{\infty} = p + \frac{p}{2} + \frac{p}{4} + \dots$ , where $p \in Z^{+}$ . Find the greatest integer value of $p$ such that $S_{\infty} < R$ .

[5]

Question 4

HLPaper 1

Consider an infinite geometric series whose first two terms are $4 lo g_{2} y, lo g_{2} y$ , where $y > 0$ . An arithmetic sequence begins with $lo g_{2} y, lo g_{2} (\frac{y}{2}), lo g_{2} (\frac{y}{4})$ , where $y > 0$ . Let $S_{12}$ be the sum of the first 12 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 $\frac{16}{3} lo g_{2} y$ .

[2]

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

[4]

Verify that $S_{12} = 12 lo g_{2} y - 66$ .

[2]

If $S_{12}$ equals exactly $\frac{3}{4}$ of the sum to infinity of the geometric sequence, solve for $y$ in the form $2^{p}$ , where $p \in Q$ .

[3]

Question 5

SLPaper 2

A theatre is installing seats in rows on a temporary stand. The numbers of seats in the first three rows are shown in the table.

Row number	1	2	3
Seats in row	16	20	24

Each new row has $4$ more seats than the row in front. The theatre has $1500$ seats available and will install only complete rows.

Determine the number of seats in the $15$ th row.

[3]

Derive the formula for the total number of seats, $S_{n}$ , in the first $n$ rows, showing that $S_{n} = 2 n^{2} + 14 n$ .

[3]

Hence, calculate the total number of seats needed for a stand with $20$ rows.

[2]

Calculate the maximum number of complete rows the theatre can install.

[3]

Each seat, including spacing, requires $0.54 m^{2}$ of floor area. Determine the total floor area of the completed stand if the theatre installs the greatest possible number of full rows. Give your answer to the nearest $m^{2}$ .

[4]

IB Mathematics Applications & Interpretation SL 1.2—sequences and Sigma Notation Questionbank

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IB Mathematics Applications & Interpretation SL 1.2—sequences and Sigma Notation Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 1.2—sequences and Sigma Notation Questionbank

Unlock all 35 questions with a free account