IB Questionbank

User interface language: English | Español

Date	November 2012	Marks available	2	Reference code	12N.2.sl.TZ0.1
Level	SL only	Paper	2	Time zone	TZ0
Command term	Find	Question number	1	Adapted from	N/A

Question

The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 .

Find the common difference.

[2]

The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 .

Find the 28^thterm of the sequence.

[2]

The first three terms of an arithmetic sequence are $5$ , $6.7$ , $8.4$ .

Find the sum of the first 28 terms.

[2]

Markscheme

valid method (M1)

e.g. subtracting terms, using sequence formula

$d = 1.7$ A1 N2

[2 marks]

correct substitution into term formula (A1)

e.g. $5 + 27(1.7)$

28^th term is 50.9 (exact) A1 N2

[2 marks]

correct substitution into sum formula (A1)

e.g. ${S_{28}} = \frac{{28}}{2}(2(5) + 27(1.7))$ , $\frac{{28}}{2}(5 + 50.9)$

${S_{28}} = 782.6$ (exact) [ $782$ , $783$ ] A1 N2

[2 marks]

Examiners report

Most candidates performed well on this question. A few were confused between the term number and the value of a term.

Syllabus sections

Topic 1 - Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.

Show 92 related questions

08N.1.sl.TZ0.1b: Consider the infinite geometric sequence...
SPNone.2.sl.TZ0.1a: Find the common difference.
11N.2.sl.TZ0.8b(i) and (ii): Consider an arithmetic sequence with n terms, with first term ( $- 36$ ) and eighth term...
11M.2.sl.TZ1.3a: Find the value of the common difference.
13N.1.sl.TZ0.9a(ii): Hence, show that $m$ satisfies the equation ${m^2} + 3m - 40 = 0$ .
13N.1.sl.TZ0.9c(ii): The sequence has a finite sum. Calculate the sum of the sequence.
15M.1.sl.TZ1.10c: Find the probability that Ann wins the game.
15N.1.sl.TZ0.7: An arithmetic sequence has the first term $\ln a$ and a common difference $\ln 3$ . The...
16N.1.sl.TZ0.9b: Show that the sum of the infinite sequence is $4{\log _2}x$ .
17N.1.sl.TZ0.2c: Find the sum of the first ten terms.
17N.1.sl.TZ0.2b: Find the tenth term.
17N.1.sl.TZ0.10a: The following diagram shows [AB], with length 2 cm. The line is divided into an infinite...
10N.1.sl.TZ0.1b: Find ${u_6}$ .
14M.1.sl.TZ1.2a: Find the common difference.
14M.1.sl.TZ1.2b: Find the first term.
13N.1.sl.TZ0.9a(i): Write down an expression for the common ratio, $r$ .
13M.2.sl.TZ1.1c: Given that ${u_n} = 1502$ , find the value of $n$ .
15M.2.sl.TZ1.3a: Write down the value of the common difference.
15M.2.sl.TZ2.6: Ramiro walks to work each morning. During the first minute he walks $80$ metres. In each...
14N.1.sl.TZ0.2a: Find the common difference.
14N.1.sl.TZ0.2c: Find the sum of the first eight terms of the sequence.
14N.1.sl.TZ0.2b: Find the eighth term.
15N.2.sl.TZ0.4b: Find the value of ${S_6}$ .
17M.1.sl.TZ2.1a: Find the common difference.
08N.1.sl.TZ0.1a: Consider the infinite geometric sequence...
08M.2.sl.TZ2.1c: Find the exact sum of the infinite sequence.
12M.2.sl.TZ1.1b(i) and (ii): (i) Show that ${S_n} = 2{n^2} + 34n$ . (ii) Hence, write down the value of...
14M.1.sl.TZ1.10b: The process described above is repeated. Find ${A_6}$ .
13M.2.sl.TZ1.1b: Find (i) ${u_{100}}$ ; (ii) ${S_{100}}$ .
14N.2.sl.TZ0.9a: (i) Find the common ratio. (ii) Hence or otherwise, find ${u_5}$ .
16M.1.sl.TZ1.4b: Find the total number of line segments in the first 200 figures.
12M.2.sl.TZ2.3b: The first term of a geometric sequence is 200 and the sum of the first four terms is...
09M.2.sl.TZ2.5b: (i) Find the value of $\sum\limits_{r = 4}^{30} {{2^r}}$ . (ii) Explain why...
10N.2.sl.TZ0.3a: Write down the common difference.
10N.2.sl.TZ0.3b(i) and (ii): (i) Given that the nth term of this sequence is 115, find the value of n . (ii) For...
11M.2.sl.TZ1.3b: Find the value of n .
11M.1.sl.TZ2.1c: Find ${S_{20}}$ .
14M.1.sl.TZ1.10c: Consider an initial square of side length $k {\text{ cm}}$ . The process described above is...
13M.2.sl.TZ1.1a: Write down the value of $d$ .
16M.2.sl.TZ2.1a: Find the common difference.
12N.2.sl.TZ0.1c: The first three terms of an arithmetic sequence are $5$ , $6.7$ , $8.4$ . Find the sum...
12M.2.sl.TZ1.1a(i) and (ii): (i) Write down the value of d . (ii) Find ${u_8}$ .
10N.1.sl.TZ0.1a: Write down the value of r .
10N.1.sl.TZ0.1c: Find the sum to infinity of this sequence.
09M.2.sl.TZ1.1a: Find the common difference.
09M.2.sl.TZ1.6a: Find the value of $r$ .
10M.2.sl.TZ1.2a: Write down the common difference.
10M.2.sl.TZ1.2c: Find the sum of the sequence.
SPNone.2.sl.TZ0.1b: Find the value of the 78th term.
11N.2.sl.TZ0.8a(i) and (ii): Consider an infinite geometric sequence with ${u_1} = 40$ and $r = \frac{1}{2}$ . (i) ...
14M.1.sl.TZ1.2c: Find the sum of the first 20 terms of the sequence.
14M.1.sl.TZ2.7b: Find a general expression for ${u_n}$ .
13N.1.sl.TZ0.9c(i): The sequence has a finite sum. State which value of $r$ leads to this sum and justify your...
16N.1.sl.TZ0.9d: Show that ${S_{12}} = 12{\log _2}x - 66$ .
17M.1.sl.TZ1.7a: Find the common ratio.
08M.1.sl.TZ1.3a: Consider the arithmetic sequence $2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots$ ...
08M.1.sl.TZ1.3b: Consider the arithmetic sequence $2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots$ ...
08M.2.sl.TZ2.1a: Find the common ratio.
08M.2.sl.TZ2.1b: Find the 10th term.
09N.2.sl.TZ0.1: In an arithmetic sequence, ${S_{40}} = 1900$ and ${u_{40}} = 106$ . Find the value of...
09M.2.sl.TZ1.6b: Find the smallest value of n for which ${S_n} > 40$ .
10M.2.sl.TZ2.2a: Find ${u_1}$ .
13M.2.sl.TZ2.5: The sum of the first three terms of a geometric sequence is $62.755$ , and the sum of the...
14M.1.sl.TZ2.7a: Given that ${u_1} = 1 + k$ , find ${u_2},{\text{ }}{u_3}$ and ${u_4}$ .
13N.1.sl.TZ0.9b(ii): Find the possible values of $r$ .
15M.2.sl.TZ1.3b: Find the first term.
16M.2.sl.TZ2.1b: Find the 30th term of the sequence.
16M.1.sl.TZ2.4: Three consecutive terms of a geometric sequence are $x - 3$ , 6 and $x + 2$ . Find the...
16M.1.sl.TZ1.4a: Given that Figure $n$ contains 801 line segments, show that $n = 200$ .
16N.1.sl.TZ0.9c: Find $d$ , giving your answer as an integer.
17M.1.sl.TZ1.7b: Solve $\sum\limits_{k = 1}^\infty {{2^{5 - k}}\ln x = 64}$ .
17M.1.sl.TZ2.1b: Find the tenth term.
17M.2.sl.TZ2.5: Consider a geometric sequence where the first term is 768 and the second term is 576. Find...
12M.2.sl.TZ2.3a: The first term of a geometric sequence is 200 and the sum of the first four terms is...
09M.2.sl.TZ1.1b: Find the value of the 78th term.
10M.2.sl.TZ2.2b(i) and (ii): (i) Given that ${u_n} = 516$ , find the value of n . (ii) For this value of n ,...
11N.2.sl.TZ0.8c: The sum of the infinite geometric sequence is equal to twice the sum of the arithmetic...
11M.1.sl.TZ2.1a: Find d .
15M.2.sl.TZ1.3c: Find the sum of the first 50 terms of the sequence.
17N.1.sl.TZ0.10b: The following diagram shows [CD], with length $b{\text{ cm}}$ , where $b > 1$ . Squares...
12N.2.sl.TZ0.1a: The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 . Find the common difference.
08M.2.sl.TZ2.10a(i) and (ii): (i) Find the number of taxis in the city at the end of 2005. (ii) Find the year in...
10M.2.sl.TZ1.2b: Find the number of terms in the sequence.
11M.1.sl.TZ2.1b: Find ${u_{20}}$ .
14M.1.sl.TZ1.10a: The following table gives the values of ${x_n}$ and ${A_n}$ , for...
13N.1.sl.TZ0.9b(i): Find the two possible values of $m$ .
15N.2.sl.TZ0.4a: Find the value of $r$ .
16N.1.sl.TZ0.9a: Find $r$ .
16M.2.sl.TZ2.1c: Find the sum of the first 30 terms.
16M.2.sl.TZ1.6: In a geometric sequence, the fourth term is 8 times the first term. The sum of the first 10...
17M.1.sl.TZ2.1c: Find the sum of the first ten terms of the sequence.
17N.1.sl.TZ0.2a: Find the common difference.

Hide related questions

Question

Markscheme

Examiners report

Syllabus sections

View options