nth Term of an Arithmetic Sequence - SSAT Upper Level Quantitative

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Find the next term of the arithmetic sequence:

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

An arithmetic sequence begins as follows:

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

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The common difference of the sequence is

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

$n > 302.7 \div 2.7 \approx 112.1$

The first negative term is the one hundred thirteenth term.

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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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

To find out the minimum value for which , 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.

What is the value of x in the sequence below?

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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}$$

Find the next term of the arithmetic sequence:

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

Find the next term in the following arithmetic sequence:

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

Find the next term in the following arithmetic sequence:

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

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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}$=3$

Find the next number in this arithmetic sequence:

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

Find the next term in this arithmetic sequence:

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

Find the next term of this arithmetic sequence:

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

Find the next term of the arithmetic sequence:

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

Find the next term of the arithmetic sequence:

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

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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}$=10$

Find the next term of the arithmetic sequence:

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

Find the next term of the arithmetic sequence:

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

Find the next term of the arithmetic sequence:

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

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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The first term is ; the common difference is

.

The hundredth term is

.

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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The first term is .

The common difference is

.

The seventieth term is

.

An arithmetic sequence begins as follows:

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

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The common difference of the sequence is

,

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The first positive term is the fortieth term.

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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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

To find out the minimum value for which , 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.

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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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

To find out the minimum value for which , 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.