ARITHMETIC SEQUENCES WORKSHEET

Problem 1 : 

15, 10, 5, 0, ........

Problem 2 : 

2, 5, 10, 17, ........

Problem 3 : 

-3/4, -1/4, 1/4, 3/4, ........

Problem 4 : 

-4, -2, 1, 5, ........

Problem 5 :

25^th term : 6, 2, -2, -6,.........

Problem 6 :

16^th term : a₁ = 8; d = 5

Problem 7 :

60^th term : 11, 5, -1, -7,.........

Problem 8 :

12^th term : a₁ = 4.2; d = 1.4

Problem 9 :

The odometer on a car reads 60,180 on day 1. Every day, the car is driven 60 miles. If this pattern continues, what is the odometer reading on day 22?

Problem 10 :

Each time a truck stops, it drops off 250 pounds of cargo. After stop 1, its cargo weighed 2000 pounds. How much does the load weigh after stop 6?

Detailed Answer Key

1. Answer : 

Step 1 :

15, 10, 5, 0, ........

Find the difference between successive terms.

10 - 15  =  -5

5 - 10  =  -5

0 - 5  =  -5

The common difference is -5.

Step 2 :

Use the common difference to find the next 3 terms.

Add -5 to each term to find the next term.

a_n  =  a_n-1 + d

0 + (-5)  =  0 - 5  =  -5

-5 + (-5)  =  -5 - 5  =  -10

-10 + (-5)  =  -10 - 5  =  -15

The sequence appears to be an arithmetic sequence with a common difference of -5.

The next 3 terms are -5, -10, -15.

2. Answer : 

2, 5, 10, 17, ........

Find the difference between successive terms.

5 - 2  =  3

10 - 5  =  5

17 - 10  =  7

The difference between successive terms is not the same.

This sequence is not an arithmetic sequence.

3. Answer : 

Step 1 :

-3/4, -1/4, 1/4, 3/4, ........

Find the difference between successive terms.

-1/4 - (-3/4)  =  1/2

1/4 - (-1/4)  =  1/2

3/4 - 1/4  =  1/2

The common difference is 1/2.

Step 2 :

Use the common difference to find the next 3 terms.

Add 1/2 to each term to find the next term.

a_n  =  a_n-1 + d

3/4 + 1/2  =  3/4 + 2/4  =  5/4

5/4 + 1/2  =  5/4 + 2/4  =  7/4

7/4 + 1/2  =  7/4 + 2/4  =  9/4  

The sequence appears to be an arithmetic sequence with a common difference of 1/2.

The next 3 terms are 5/4, 7/4, 9/4.

4. Answer : 

-4, -2, 1, 5, ........

Find the difference between successive terms.

-2 - (-4)  =  2

1 - (-2)  =  3

5 - 1  =  4

The difference between successive terms is not the same.

This sequence is not an arithmetic sequence.

5. Answer : 

Step 1 : Find the common difference.

2 - 6  =  -4

-2 - 2  =  -4

-6 - (-2)  =  -4

The common difference is -4.

Step 2 : Find the 25^th term.

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 6 for a₁, 25 for n, and -4 for d.

a₂₅  =  6 + (25 - 1)(-4)

Simplify the expression in parentheses.

a₂₅  =  6 + (24)(-4)

Multiply. 

a₂₅  =  6 - 96

Subtract. 

a₂₅  =  -90

6. Answer : 

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 8 for a₁, 16 for n, and 5 for d.

a₁₆  =  8 + (16 - 1)(5)

Simplify the expression in parentheses.

a₁₆  =  8 + (15)(5)

Multiply. 

a₁₆  =  8 + 75

Add. 

a₁₆  =  83

7. Answer : 

Step 1 : Find the common difference.

5 - 11  =  -6

-1 - 5  =  -6

-7 - (-1)  =  -6

The common difference is -6.

Step 2 : Find the 60^th term.

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 11 for a₁, 60 for n, and -6 for d.

a₆₀  =  11 + (60 - 1)(-6)

Simplify the expression in parentheses.

a₆₀  =  11 - (59)(-6)

Multiply. 

a₆₀  =  11 - 354

Subtract. 

a₆₀  =  -343

8. Answer : 

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 4.2 for a₁, 12 for n, and 1.4 for d.

a₁₂  =  4.2 + (12 - 1)(1.4)

Simplify the expression in parentheses.

a₁₂  =  4.2 + (11)(1.4)

Multiply. 

a₁₂  =  4.2 + 15.4

Add. 

a₁₂  =  19.6

9. Answer : 

Notice that the sequence for the situation is arithmetic with d = 60 because the odometer reading will increase by 60 miles per day. Since the odometer reading on day 1 is 60,180 miles, a₁ = 60,180. Because you want to find the odometer reading on day 22, you will need to find the 20^th term of the sequence, so n = 22.

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 60,180 for a₁, 22 for n, and 60 for d.

a₂₂  =  60,180 + (22 - 1)(60)

Simplify the expression in parentheses.

a₂₂  =  60,180 + (21)(60)

Multiply. 

a₂₂  =  60,180 + 1,260

Add. 

a₂₂  =  61,440

The odometer will read 61,440 miles on day 22.

10. Answer : 

Notice that the sequence for the situation is arithmetic with d = -250, because the truck drops off 250 pounds each time it stops. Because cargo weighed 2000 pounds after stop 1, a₁ = 2000. Because you want to find the weight after stop 6, you will need to find the 6^th term of the sequence, so n = 6.

Write the rule to find the n^th term.  

a_n  =  a₁ + (n - 1)d

Substitute 2000 for a₁, 6 for n, and -250 for d.

a₆  =  2000 + (6 - 1)(-250)

Simplify the expression in parentheses.

a₆  =  2000 + (5)(-250)

Multiply. 

a₆  =  2000 - 1250

Subtract. 

a₆  =  750

The load weighs 750 pounds after stop 6. 

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