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ACT Math : nth Term of an Arithmetic Sequence

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Example Questions

Example Question #1 : Arithmetic Sequences

If the first day of the year is a Monday, what is the 295th day?

Possible Answers:

Wednesday

Monday

Tuesday

Saturday

Correct answer:

Monday

Explanation:

The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.

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Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

If the first two terms of a sequence are $\small \pi$ and $\small 2\pi ^{2}$ , what is the 38th term?

Possible Answers:

$\small 2\pi ^{37}$

$\small 2^{38}\pi ^{38}$

$\small 2\pi ^{38}$

$\small 2^{37}\pi ^{38}$

$\small 2^{37}\pi ^{37}$

Correct answer:

$\small 2^{37}\pi ^{38}$

Explanation:

The sequence is multiplied by $\small 2\pi$ each time.

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Example Question #1 : Arithmetic Sequences

Find the 10th term of the following sequence:

-3,-15,-27,-39,...

Possible Answers:

$a_{10}=-113$

$a_{10}=-99$

$a_{10}=-125$

$a_{10}=-123$

$a_{10}=-111$

Correct answer:

$a_{10}=-111$

Explanation:

The formula for finding the $n^{th}$ term of an arithmetic sequence is as follows:

a_n=a_1+d(n-1)

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the 10th term:

$a_{10}=-3+(-12)(10-1)$

$a_{10}=-3+(-12)(9)$

$a_{10}=-3-108$

$a_{10}=-111$

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Example Question #3 : Arithmetic Sequences

What is the rd term of the following sequence: 17,24,31,38,... ?

Possible Answers:

589

711

651

579

661

Correct answer:

661

Explanation:

Notice that between each of these numbers, there is a difference of ; however the first number is 10 + 7 , the second 10 + 7 * 2 , and so forth. This means that for each element, you know that the value must be 10 + 7*n , where is that number's place in the sequence. Thus, for the rd element, you know that the value will be 10 + 7*93 = 10 + 651 or 661 .

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Example Question #2 : Arithmetic Sequences

What is the th term in the following series of numbers: 4,10,16,22,... ?

Possible Answers:

116

120

172

118

148

Correct answer:

118

Explanation:

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is 6-2 or . The second is 6*2-2 or , and so forth... Therefore, for the th element, the value will be 6*20-2 or 118 .

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Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is and whose ninth term is .

Possible Answers:

117

123

Correct answer:

Explanation:

Use the formula a_n = a₁ + (n – 1)d

a₆ = a₁ + 5d

a₉ = a₁ + 8d

Subtracting these equations yields

a₆– a₉ = –3d

–7 – 8 = –3d

d = 5

a₁ = 33

Then use the formula for the series; = –30

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Example Question #4 : Nth Term Of An Arithmetic Sequence

Given the sequence of numbers:

1, 5, 9, _ , _ , 21 ....

What are the two missing terms of the arithmetic sequence?

Possible Answers:

13, 16

14, 17

14, 16

12, 18

13, 17

Correct answer:

13, 17

Explanation:

The sequence is defined by a_n= 4n – 3 for such n = 1,2,3,4....

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Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

What is the next term in the following sequence?

$\left \{ 4,11,18,25,32... \right \}$

Possible Answers:

Correct answer:

Explanation:

What is the next term in the following sequence?

$\left \{ 4,11,18,25,32... \right \}$

This is an arithmetic sequence with a common difference of . To find the next term in an arithmetic sequence, add the common difference to the previously listed term:

32+7=39

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Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Find the sixth term in the following number sequence.

3,7,11...

Possible Answers:

Correct answer:

Explanation:

This question can be answered by analyzing the sequence provided and determining the pattern. The first term is , and the second term is The third term is 11. Thus, has been added to in order to obtain , and has been added to in order to obtain 11. This shows that is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.

3,7,11,15,19,23

Thus, the sixth term is 23.

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Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

What is the next term of the series 4,11,9,16,14 ?

Possible Answers:

Correct answer:

Explanation:

Begin by looking at the transitions from number to number in this series:

From to : Add

From to : Subtract

From to : Add

From to : Subtract

From what you can tell, you can guess that the next step will be to add . Thus, the next value will be .

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ACT Math : nth Term of an Arithmetic Sequence

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Arithmetic Sequences

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #1 : Arithmetic Sequences

Example Question #3 : Arithmetic Sequences

Example Question #2 : Arithmetic Sequences

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #4 : Nth Term Of An Arithmetic Sequence

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

All ACT Math Resources

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