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SAT II Math II : Sequences

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Example Question #11 : Sequences

An arithmetic sequence begins as follows:

$\frac{5}{12}, 0.45,...$

Give the tenth term.

Possible Answers:

$\frac{43}{60}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{11}{15}$

$\frac{7}{10}$

Correct answer:

$\frac{43}{60}$

Explanation:

Rewrite 0.45 as a fraction:

$0.45 = \frac{45}{100} = \frac{9}{20}$

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1} = \frac{9}{20} - \frac{5}{12} = \frac{27}{60} - \frac{25}{60} = \frac{2}{60} = \frac{1}{30}$

The th term of an arithmetic sequence can be found using the formula

$a_{n} = a_{1} + (n-1)d$ .

Setting $n = 10, a_{1} = \frac{5}{12} , d = \frac{1}{30}$ :

$a_{10} = \frac{5}{12} + (10-1) \cdot \frac{1}{30}$

$= \frac{5}{12} + 9 \cdot \frac{1}{30}$

$= \frac{5}{12} + \frac{3}{10}$

$= \frac{25}{60} + \frac{18}{60}$

$= \frac{43}{60}$ ,

the correct response.

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Example Question #111 : Mathematical Relationships

An arithmetic sequence begins as follows:

$\frac{3}{4} , \frac{13}{16} , \frac{7}{8},...$

Give the eighteenth term of the sequence.

Possible Answers:

$1 \frac{13}{16}$

$1\frac{3}{4}$

$1\frac{15}{16}$

$1\frac{7}{8}$

Correct answer:

$1 \frac{13}{16}$

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d= a_{2} - a_{1}$

Setting $a_{1} = \frac{3}{4}, a_{2} = \frac{13}{16}$ :

$d = \frac{13}{16} - \frac{3}{4} = \frac{13}{16} - \frac{12}{16} = \frac{1 }{16}$

The th term of an arithmetic sequence can be calculated using the formula

$a_{n} = a_{1} + (n- 1)d$

The eighteenth term can be found by setting $a_{1} = \frac{3}{4} = \frac{12}{16},n = 18, d = \frac{1 }{16}$ and evaluating:

$a_{18} = \frac{12}{16} + (18- 1) \frac{1}{16}$

$= \frac{12}{16}+ 17 \cdot \frac{1}{16}$

$= \frac{12}{16} + 17 \cdot \frac{1}{16}$

$= \frac{12}{16} + \frac{17}{16}$

$= \frac{29}{16}$

$=1 \frac{13}{16}$

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SAT II Math II : Sequences

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

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Example Question #11 : Sequences

Example Question #111 : Mathematical Relationships

All SAT II Math II Resources

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