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Mathematics LibreTexts

14.3E: Exercises

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Practice Makes Perfect

Exercise 14.3E.17 Determine if a Sequence is Arithmetic

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

  1. 4,12,20,28,36,44,
  2. 7,2,3,8,13,18,
  3. 15,16,3,12,21,30,
  4. 11,5,1,713,19,
  5. 8,5,2,1,4,7,
  6. 15,5,5,15,25,35,
Answer

1. The sequence is arithmetic with common difference d=8.

3. The sequence is not arithmetic.

5. The sequence is arithmetic with common difference d=3.

Exercise 14.3E.18 Determine if a Sequence is Arithmetic

In the following exercises, write the first five terms of each sequence with the given first term and common difference.

  1. a1=11 and d=7
  2. a1=18 and d=9
  3. a1=7 and d=4
  4. a1=8 and d=5
  5. a1=14 and d=9
  6. a1=3 and d=3
Answer

1. 11,18,25,32,39

3. 7,3,1,5,9

5. 14,5,4,13,22

Exercise 14.3E.19 Find the General Term (nthe Term) of an Arithmetic Sequence

In the following exercises, find the term described using the information provided.

  1. Find the twenty-first term of a sequence where the first term is three and the common difference is eight.
  2. Find the twenty-third term of a sequence where the first term is six and the common difference is four.
  3. Find the thirtieth term of a sequence where the first term is 14 and the common difference is five.
  4. Find the fortieth term of a sequence where the first term is 19 and the common difference is seven.
  5. Find the sixteenth term of a sequence where the first term is 11 and the common difference is 6.
  6. Find the fourteenth term of a sequence where the first term is eight and the common difference is 3.
  7. Find the twentieth term of a sequence where the fifth term is 4 and the common difference is 2. Give the formula for the general term.
  8. Find the thirteenth term of a sequence where the sixth term is 1 and the common difference is 4. Give the formula for the general term.
  9. Find the eleventh term of a sequence where the third term is 19 and the common difference is five. Give the formula for the general term.
  10. Find the fifteenth term of a sequence where the tenth term is 17 and the common difference is seven. Give the formula for the general term.
  11. Find the eighth term of a sequence where the seventh term is 8 and the common difference is 5. Give the formula for the general term.
  12. Find the fifteenth term of a sequence where the tenth term is 11 and the common difference is 3. Give the formula for the general term.
Answer

1. 163

3. 131

5. 79

7. a20=34. The general term is an=2n+6.

9. a11=59. The general term is an=5n+4.

11. a8=13. The general term is an=5n+27.

Exercise 14.3E.20 Find the General Term (nthe Term) of an Arithmetic Sequence

In the following exercises, find the first term and common difference of the sequence with the given terms. Give the formula for the general term.

  1. The second term is 14 and the thirteenth term is 47.
  2. The third term is 18 and the fourteenth term is 73.
  3. The second term is 13 and the tenth term is 51.
  4. The third term is four and the tenth term is 38.
  5. The fourth term is 6 and the fifteenth term is 27.
  6. The third term is 13 and the seventeenth term is 15.
Answer

1. a1=11,d=3. The general term is an=3n+8.

3. a1=21,d=8. The general term is an=8n+29

5. a1=15,d=3. The general term is an=3n18.

Exercise 14.3E.21 Find the Sum of the First n Terms of an Arithmetic Sequence

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.

  1. 11,14,17,20,23,
  2. 12,18,24,30,36,
  3. 8,5,2,1,4,
  4. 16,10,4,2,8,
  5. 17,15,13,11,9,
  6. 15,12,9,6,3,
Answer

1. 1,635

3. 1,065

5. 360

Exercise 14.3E.22 Find the Sum of the First n Terms of an Arithmetic Sequence

In the following exercises, find the sum of the first 50 terms of the arithmetic sequence whose general term is given.

  1. an=5n1
  2. an=2n+7
  3. an=3n+5
  4. an=4n+3
Answer

1. 6,325

3. 3,575

Exercise 14.3E.23 Find the Sum of the First n Terms of an Arithmetic Sequence

In the following exercises, find each sum.

  1. 40i=1(8i7)
  2. 45i=1(7i5)
  3. 50i=1(3i+6)
  4. 25i=1(4i+3)
  5. 35i=1(6i2)
  6. 30i=1(5i+1)
Answer

1. 6,280

3. 4,125

5. 3,580

Exercise 14.3E.24 Writing Exercises
  1. In your own words, explain how to determine whether a sequence is arithmetic.
  2. In your own words, explain how the first two terms are used to find the tenth term. Show an example to illustrate your explanation.
  3. In your own words, explain how to find the general term of an arithmetic sequence.
  4. In your own words, explain how to find the sum of the first n terms of an arithmetic sequence without adding all the terms.
Answer

1. Answer may vary

3. Answer may vary

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This figure shows a chart with four rows and four columns. The first row is the header row and reads, “I can”, “Confidently”, “With some help”, and “No, I don’t get it!” The column, beginning with second row reads 1. Determine if a Sequence is Arithmetic, 2. Find the General Term (nth term) of Arithmetic Sequence, and 3. Find the sum of the first Terms of an Arithmetic Sequence”. The remaining columns are blank.
Figure 12.2.29

b. After reviewing this checklist, what will you do to become confident for all objectives?


This page titled 14.3E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Chau D Tran.

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