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GED Math : Patterns and Sequences

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Example Questions

Example Question #1 : Patterns And Sequences

What is the next number in the series?

$\displaystyle 1, 3, 7, 15, 31,...$

Possible Answers:

$\displaystyle 63$

127 $\displaystyle 127$

$\displaystyle 47$

Correct answer:

$\displaystyle 63$

Explanation:

To pattern uses the formula $\small \small x_n=2x_{n-1}+1$ $\displaystyle \small \small x_n=2x_{n-1}+1$.

$\small x_6=2(31)+1=62+1=63$ $\displaystyle \small x_6=2(31)+1=62+1=63$

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Example Question #1 : Patterns And Sequences

What is the next number in the sequence?

$\small 9,7,5,3,1,...$ $\displaystyle \small 9,7,5,3,1,...$

Possible Answers:

$\small 0$ $\displaystyle \small 0$

$\small -1$ $\displaystyle \small -1$

$\small 1$ $\displaystyle \small 1$

$\small 2$ $\displaystyle \small 2$

Correct answer:

$\small -1$ $\displaystyle \small -1$

Explanation:

The pattern follows this equation:

$\small x_n=x_{n-1}-2$ $\displaystyle \small x_n=x_{n-1}-2$

$\small x_n=1-2=-1$ $\displaystyle \small x_n=1-2=-1$

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Example Question #3 : Patterns And Sequences

What property of arithmetic is symbolized below?

If $\bigstar = \blacksquare$ $\displaystyle \bigstar = \blacksquare$, then $\blacksquare = \bigstar$ $\displaystyle \blacksquare = \bigstar$

Possible Answers:

Associative

Commutative

Symmetric

Reflexive

Correct answer:

Symmetric

Explanation:

The symbols show that if one number is equal to another, the equality holds no matter the order of the two. This is the symmetric property of equality.

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Example Question #4 : Patterns And Sequences

What property of arithmetic is symbolized below?

$\blacklozenge = \blacklozenge$ $\displaystyle \blacklozenge = \blacklozenge$

Possible Answers:

Reflexive

Transitive

Commutative

Identity

Correct answer:

Reflexive

Explanation:

The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.

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Example Question #4 : Patterns And Sequences

What property of arithmetic is symbolized below?

$\blacksquare +\left ( \blacktriangle + \blacktriangledown \right ) =\left ( \blacksquare + \blacktriangle \right )+ \blacktriangledown$ $\displaystyle \blacksquare +\left ( \blacktriangle + \blacktriangledown \right ) =\left ( \blacksquare + \blacktriangle \right )+ \blacktriangledown$

Possible Answers:

Associative

Transitive

Commutative

Symmetric

Correct answer:

Associative

Explanation:

The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.

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Example Question #1 : Patterns And Sequences

What number replaces the circle in the following sequence?

$5, 7, 11, 17, 25, 35,\bigcirc...$ $\displaystyle 5, 7, 11, 17, 25, 35,\bigcirc...$

Possible Answers:

$\displaystyle 49$

$\displaystyle 47$

$\displaystyle 50$

$\displaystyle 45$

Correct answer:

$\displaystyle 47$

Explanation:

Add 2 to the first number to get the second; each subsequent increment is increased by 2. The pattern:

$\displaystyle 5 + 2 = 7$

$\displaystyle 7 + 4 = 11$

$\displaystyle 11 + 6 = 17$

$\displaystyle 17+ 8 = 25$

$\displaystyle 25 + 10 = 35$

Add 12 to get the next element:

$\displaystyle 35 + 12 = 47$, which is the correct choice.

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Example Question #171 : Numbers

What number replaces the circle in this sequence?

$4, 6, 10, 16, 26, 42, 68, \bigcirc$ $\displaystyle 4, 6, 10, 16, 26, 42, 68, \bigcirc$

Possible Answers:

110 $\displaystyle 110$

102 $\displaystyle 102$

$\displaystyle 94$

126 $\displaystyle 126$

Correct answer:

110 $\displaystyle 110$

Explanation:

After the first two elements, each subsequent element is the sum of the previous two (similar to the Fibonacci sequence).

The third and subsequent elements are calculated as follows:

$\displaystyle 4 + 6 = 10$

$\displaystyle 6 + 10 = 16$

$\displaystyle 10 + 16 = 26$

$\displaystyle 16 + 26 = 42$

$\displaystyle 26 + 42 = 68$

$\displaystyle 42 + 68 = 110$, the correct response.

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Example Question #6 : Patterns And Sequences

What number replaces the circle in the following sequence?

$1, -4, 9, -16, 25, -36, \bigcirc...$ $\displaystyle 1, -4, 9, -16, 25, -36, \bigcirc...$

Possible Answers:

$\displaystyle -72$

$\displaystyle 72$

$\displaystyle -49$

$\displaystyle 49$

Correct answer:

$\displaystyle 49$

Explanation:

The sequence consists of the perfect square integer, except that every other element is negated. The sequence goes like this:

$1 = +1^{2}$ $\displaystyle 1 = +1^{2}$

$-4 = -2^{2}$ $\displaystyle -4 = -2^{2}$

$9 = +3^{2}$ $\displaystyle 9 = +3^{2}$

$-16 = -4^{2}$ $\displaystyle -16 = -4^{2}$

$25 = + 5^{2}$ $\displaystyle 25 = + 5^{2}$

$-36 = -6^{2}$ $\displaystyle -36 = -6^{2}$

The next entry is $+7^{2} = 49$ $\displaystyle +7^{2} = 49$.

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Example Question #5 : Patterns And Sequences

$\displaystyle ABC = 28$; $\displaystyle A$, $\displaystyle B$, and $\displaystyle C$ are distinct integers.

Which of the following could be equal to $\displaystyle A + B + C$ ?

Possible Answers:

$\displaystyle 24$

$\displaystyle 11$

$\displaystyle 17$

$\displaystyle 30$

Correct answer:

$\displaystyle 17$

Explanation:

We need to find ways to factor 28 such that the three factors are different, and then find the sum of those factors in each case.

28 can be expressed as the product of three integers four ways:

I) $1 \times 1 \times 28$ $\displaystyle 1 \times 1 \times 28$

II) $1 \times 2 \times 14$ $\displaystyle 1 \times 2 \times 14$

III) $1 \times 4 \times 7$ $\displaystyle 1 \times 4 \times 7$

IV) $2 \times 2 \times 7$ $\displaystyle 2 \times 2 \times 7$

We disregard (I) and (IV) since the factors are not distinct.

We look at (II) and (III):

II: Sum: $\displaystyle 1 + 2 + 14 = 17$

III: Sum: $\displaystyle 1 + 4 + 7 = 12$

Of the four choices, only 17 is a possible sum; that is the correct choice.

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Example Question #7 : Patterns And Sequences

What property of arithmetic is symbolized below?

If $\bigstar = \blacksquare$ $\displaystyle \bigstar = \blacksquare$ and $\blacksquare = \blacktriangle$ $\displaystyle \blacksquare = \blacktriangle$, then $\bigstar = \blacktriangle$ $\displaystyle \bigstar = \blacktriangle$.

Possible Answers:

Reflexive

Distributive

Transitive

Associative

Correct answer:

Transitive

Explanation:

The symbols express the idea that two numbers equal to the same number are also equal to each other. This is the transitive property of equality.

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All GED Math Resources

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GED Math : Patterns and Sequences

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Patterns And Sequences

Example Question #1 : Patterns And Sequences

Example Question #3 : Patterns And Sequences

Example Question #4 : Patterns And Sequences

Example Question #4 : Patterns And Sequences

Example Question #1 : Patterns And Sequences

Example Question #171 : Numbers

Example Question #6 : Patterns And Sequences

Example Question #5 : Patterns And Sequences

Example Question #7 : Patterns And Sequences

All GED Math Resources

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