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ACT Math : How to find the nth term of an arithmetic sequence

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Example Questions

Example Question #1 : Nth Term Of An Arithmetic Sequence

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

Possible Answers:

Wednesday

Saturday

Monday

Tuesday

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 : Arithmetic Sequences

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

Possible Answers:

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

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

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

$\small 2\pi ^{38}$

$\small 2\pi ^{37}$

Correct answer:

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

Explanation:

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

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Example Question #2 : Arithmetic Sequences

Find the 10th term of the following sequence:

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

Possible Answers:

$a_{10}=-99$

$a_{10}=-113$

$a_{10}=-111$

$a_{10}=-125$

$a_{10}=-123$

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 : 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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ACT Math : How to find the nth term of an arithmetic sequence

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Nth Term Of An Arithmetic Sequence

Example Question #1 : Arithmetic Sequences

Example Question #2 : Arithmetic Sequences

Example Question #3 : Arithmetic Sequences

Example Question #2 : Arithmetic Sequences

Example Question #1 : Nth Term Of An Arithmetic Sequence

All ACT Math Resources

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