nth Term of an Arithmetic Sequence - SSAT Upper Level Quantitative

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Question

What is the value of x in the sequence below?

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Answer

In this sequence, each subsequent number is equal to one third of the preceding number.

One third of 11 is equal to:

$\frac{11}{3}=3\frac{2}{3}$

Therefore, the correct answer is: $3\frac{2}{3}$

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference for this sequence is . To find the next number in the sequence, add to the last given number.

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Question

Find the next term in the following arithmetic sequence:

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Answer

The sequence is subtracting for each term. The next term can be found by subtracting from :

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Question

Find the next term in the following arithmetic sequence:

$\frac{9}{2}, 4, \frac{7}{2}, ?$

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Answer

The common difference for this arithmetic sequence is $-\frac{1}{2}$ . To find the next term in the sequence, subtract that value from the last given value.

$\frac{7}{2}-\frac{1}{2}=3$

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Question

Find the next number in this arithmetic sequence:

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Answer

The common difference for this arithmetic sequence is . Take away from to get the next term.

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Question

Find the next term in this arithmetic sequence:

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Answer

The common difference for this sequence is . Subtract from the last given term to find the next term.

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Question

Find the next term of this arithmetic sequence:

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Answer

The common difference for this sequence is . Add this to the last given term to find the next one.

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference is . Add this to the last given term to find the next term.

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Question

Find the next term of the arithmetic sequence:

$-\frac{1}{2}, 3, \frac{13}{2}, ?$

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Answer

The common difference is $\frac{7}{2}$ . Add this to the last given term to find the next term.

$\frac{13}{2}+\frac{7}{2}=\frac{20}{2}=10$

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference is . Add this to the last given term to find the next term.

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference is . Add this to the last given term to find the next term.

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference is . Add this to the last given term to find the next term.

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Question

Find the next term of the arithmetic sequence:

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Answer

The common difference is . Add this to the last given term to find the next term.

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Question

The first two terms of an arithmetic sequence are 4 and 9, in that order. Give the one-hundredth term of that sequence.

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Answer

The first term is $x_{0} = 4$ ; the common difference is

.

The hundredth term is

$x_{99} = x_{0} + 99 d = 4 + 99 \cdot5 = 4 + 495 = 499$ .

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Question

The first two terms of an arithmetic sequence are 1,000 and 997, in that order. What is the seventieth term?

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Answer

The first term is $x_{0} = 1,000$ .

The common difference is

.

The seventieth term is

$x_{69} = x_{0}+ 69 \cdot d= 1,000 + 69 \cdot (-3)= 1,000 - 207 = 793$ .

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Question

An arithmetic sequence begins as follows:

Which of the following terms is the first positive term in the sequence?

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Answer

The common difference of the sequence is

,

so the th term of the sequence is

$a_{n} = -128 + 3.3 (n-1)$

To find out the minimum value for which $a_{n} > 0$ , set up this inequality:

The first positive term is the fortieth term.

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Question

An arithmetic sequence begins as follows:

$-78 \frac{2}{3}, -75 \frac{4}{5},...$

Which of the following terms is the first positive term in the sequence?

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Answer

The common difference of the sequence is

$-75 \frac{4}{5} - \left ( -78 \frac{2}{3} \right ) =2 \frac{13}{15}$ ,

so the th term of the sequence is

$a_{n} = - 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 0$ , set up this inequality:

$- 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) (n-1) > 0$

$- 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) n - 2\frac{13}{15} > 0$

$\left ( 2\frac{13}{15} \right ) n - 81\frac{8}{15} > 0$

$\left ( 2\frac{13}{15} \right ) n > 81\frac{8}{15}$

$n > 81\frac{8}{15} \div 2\frac{13}{15} = 28 \frac{19}{43}$

The first positive term in the sequence is the twenty-ninth term.

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Question

An arithmetic sequence begins as follows:

$155 \frac{5}{6}, 153 \frac{3}{4},...$

Which of the following terms is the first negative term in the sequence?

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Answer

The common difference of the sequence is

$153 \frac{3}{4}- 155 \frac{5}{6}= -2 \frac{1}{12}$

so the th term of the sequence is

$a_{n} = 155\frac{5}{6}-\left (2 \frac{1}{12} \right )(n-1)$

To find out the minimum value for which $a_{n} < 0$ , set up this inequality:

$155\frac{5}{6}-\left (2 \frac{1}{12} \right )(n-1) < 0$

$155\frac{5}{6}-\left (2 \frac{1}{12} \right ) n + 2\frac{1}{12} < 0$

$157\frac{11}{12}-\left (2 \frac{1}{12} \right ) n < 0$

$157\frac{11}{12} < \left (2 \frac{1}{12} \right ) n$

$\left (2 \frac{1}{12} \right ) n > 157\frac{11}{12}$

$n > 157\frac{11}{12} \div 2 \frac{1}{12} = 75 \frac{4}{5}$

The seventy-sixth term is the first negative term.

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Question

An arithmetic sequence begins as follows:

Which of the following terms is the first negative term in the sequence?

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Answer

The common difference of the sequence is

so the th term of the sequence is

$a_{n} = 300 -2.7 (n-1)$

To find out the minimum value for which $a_{n} < 0$ , set up this inequality:

$n > 302.7 \div 2.7 \approx 112.1$

The first negative term is the one hundred thirteenth term.

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Question

An arithmetic sequence begins as follows:

$1 \frac{1}{7}, 3 \frac{1}{4},...$

Which of the following is the first term greater than 100?

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Answer

The common difference of the sequence is

$3 \frac{1}{4} - 1 \frac{1}{7} = 2\frac{3}{28}$

so the th term of the sequence is

$a_{n} = 1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 100$ , set up this inequality:

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1) > 100$

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) n -2\frac{3}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n - \frac{27}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n > 100 \frac{27}{28}$

$n > 100 \frac{27}{28} \div 2\frac{3}{28} = 47 \frac{54}{59}$

The correct response is the forty-eighth term.

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