Sequences and Series - SSAT Upper Level Quantitative

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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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 common difference for the arithmetic sequence:

$-\frac{8}{3}, -\frac{2}{3}, \frac{4}{3}, \frac{10}{3}...$

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Answer

Subtract the first term from the second term to find the common difference.

$-\frac{2}{3}-\left(-\frac{8}{3}\right)=-\frac{2}{3}+\frac{8}{3}=\frac{6}{3}=2$

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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Question

Find the common difference for the arithmetic sequence:

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Answer

Subtract the first term from the second term to find the common difference.

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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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Question

Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?

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Answer

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-2 \right )+ x +\left ( x+2 \right ) = 537$

The three integers are 177, 179, and 181, and the product of the least and greatest is

$177 \times 181 = 32,037$

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Question

Which of the following can be the sum of four consecutive positive integers?

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Answer

Let , , , and be the four consecutive integers. Then their sum would be

In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.

$178 -6 = 172 ; 172 \div4 = 43$

$213 -6 = 207 ; 207 \div4 = 51 ; R ; 3$

$420 -6 = 414 ; 414 \div4 = 103 : R : 2$

$143 -6 = 137 ; 137 \div4 = 34: R: 1$

Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.

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Question

Three consecutive integers have sum . What is their product?

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Answer

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-1 \right )+ x +\left ( x+1 \right ) = 427$

$x = 142\frac{1}{3}$

This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.

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Question

Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?

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Answer

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-2 \right )+ x +\left ( x+2 \right ) = 924$

The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is

$306 \times 310= 94,860$

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Question

Four consecutive integers have sum 3,350. What is the product of the middle two?

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Answer

Call the least of the four integers . The four integers are therefore

,

and they can be found using the equation

$x + \left (x+1 \right )+\left (x+2 \right )+\left ( x+3 \right )= 3,350$

$x=3,344 \div 4 = 836$

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

$837 \times 838 = 701,406$

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Question

Three consecutive integers have a sum of . What is their product?

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Answer

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-1 \right )+ x +\left ( x+1 \right ) = 312$

The integers are therefore 103, 104, 105. The correct response is their product, which is

$103 \times 104 \times 105= 1,124,760$

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