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SSAT Upper Level Math : How to find the answer to an arithmetic sequence

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Example Questions

Example Question #1 : Arithmetic Sequences

The angle measures of a pentagon form an arithmetic sequence. The smallest angle measures $70^{\circ }$ . What does the largest angle measure?

Possible Answers:

$142^{\circ }$

$146^{\circ }$

$108^{\circ }$

$127^{\circ }$

$138^{\circ }$

Correct answer:

$146^{\circ }$

Explanation:

The measures of the five angles of a pentagon add up to 180^o (5-2) = 540^o , based on the formula 180^o(n-2) .

If the measures of the five angles form an arithmetic sequence, the angles have measures increasing by a some common difference, .

70,70+d,70+2d,70+3d,70+4d

Given this pattern and the total sum, we can solve for the common difference.

$70+ \left( 70+d\right )+\left( 70+2d\right )+\left( 70+3d\right )+\left( 70+4d\right ) = 540$

350+10d = 540

10d = 190

d=19

The greatest of the angle measures is given by 70+4d .

$70+4d = 70 + (4 )(19) = 146^{\circ }$

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Example Question #2 : Arithmetic Sequences

Hunter makes $\$4.00$ for the first hour of work, $\$6.00$ for his second hour of work, $\$8.00$ for his third hour of work, and so on. How much money will he make if he works for hours?

Possible Answers:

$\$130$

$\$154$

$\$180$

$\$24$

Correct answer:

$\$154$

Explanation:

The question is basically asking you to find the sum of the first terms of the following arithmetic sequence:

4, 6, 8...

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have
the first term of the sequence
$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 11th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=4

n=11

d=6-4=2

Now, plug in the information to find the value of the 11th term.

$y_{11}=4+(11-1)(2)=4+(10)(2)=4+20=24$

Now that we know the 11th term of the sequence, we can plug in that value into the equation for the sum to find what these first 11 terms add up to.

$\text{Sum}=\frac{11(4+24)}{2}=\frac{11(28)}{2}=154$

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Example Question #3 : Arithmetic Sequences

Find the $8^{th}$ term of the arithmetic sequence:

-8, -2, 4, 10...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=-8

n=8

d=-2-(-8)=6

Now, plug in the information to find the value of the 8th term.

y_8=-8+(8-1)6=-8+(7)6=-8+42=34

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Example Question #4 : Arithmetic Sequences

Find the $16^{th}$ term of the following arithmetic sequence:

100, 94, 88, 82...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=100

n=16

d=94-100=-6

Now, plug in the information to find the value of the 16th term.

$y_{16}=100+(-6)(16-1)=100+(-6)(15)=100-90=10$

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Example Question #1 : Other Arithmetic Sequences

Find the $9^{th}$ term of the following arithmetic sequence:

45, 49, 53, 57...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=45

n=9

d=49-45=4

Now, plug in the information to find the value of the 9th term.

y_9=45+(4)(9-1)=45+(4)(8)=45+32=77

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Example Question #2 : Other Arithmetic Sequences

Find the $12^{th}$ term of the following arithmetic sequence:

-1, 4, 9, 14...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=-1

n=12

d=-4-(-1)=5

Now, plug in the information to find the value of the 12th term.

$y_{12}=-1+(12-1)(5)=-1+(11)(5)=-1+55=54$

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Example Question #7 : Arithmetic Sequences

Find the $7^{th}$ term for the following arithmetic sequence:

18, 11, 4, -3...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=18

n=7

d=11-18=-7

Now, plug in the information to find the value of the 7th term.

y_7=18+(7-1)(-7)=18+(6)(-7)=18-42=-24

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Example Question #1 : Arithmetic Sequences

Find the $10^{th}$ term of the following arithmetic sequence:

-15, -7, 1, 9...

Possible Answers:

Correct answer:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

For this sequence,

a_1=-15

n=10

d=-7-(-15)=8

Now, plug in the information to find the value of the 10th term.

$y_{10}=-15+(8)(10-1)=-15+(8)(9)=-15+72=57$

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Example Question #9 : Arithmetic Sequences

Brandon is improving very quickly at math. He improves at a rate of points per test. If he scored a on his first test, on his second test, and on his third test, what score will he get on his $8^{th}$ test?

Possible Answers:

Correct answer:

Explanation:

You should recognize this as an arithmetic sequence:

42, 44, 46...

The question is asking you to find the 8th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=42

n=8

d=2

Now, plug in the information to find the value of the 8th term.

y_8=42+(8-1)(2)=42+(7)(2)=42+14=56

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Example Question #1 : How To Find The Answer To An Arithmetic Sequence

Julia gets better every time she plays basketball. In her first game, she scored points. In her second game, she scored points, and in her third game, she scored points. If she continues to improve her basketball skills at this same pace, how many points should she be scoring by her $12^{th}$ game?

Possible Answers:

Correct answer:

Explanation:

You should recognize this as an arithmetic sequence:

8, 12, 16...

The question is asking you to find the 12th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=8

n=12

d=4

Now, plug in the information to find the value of the 12th term.

$y_{12}=8+(12-1)(4)=8+(11)(4)=8+44=52$

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SSAT Upper Level Math : How to find the answer to an arithmetic sequence

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Arithmetic Sequences

Example Question #2 : Arithmetic Sequences

Example Question #3 : Arithmetic Sequences

Example Question #4 : Arithmetic Sequences

Example Question #1 : Other Arithmetic Sequences

Example Question #2 : Other Arithmetic Sequences

Example Question #7 : Arithmetic Sequences

Example Question #1 : Arithmetic Sequences

Example Question #9 : Arithmetic Sequences

Example Question #1 : How To Find The Answer To An Arithmetic Sequence

All SSAT Upper Level Math Resources

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