# ARITHMETIC SEQUENCES WORKSHEET

Problem 1-4 : Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

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, ........

Problems 5-8 : Find the indicated term of each arithmetic sequence.

Problem 5 :

25th term : 6, 2, -2, -6,.........

Problem 6 :

16th term : a1 = 8; d = 5

Problem 7 :

60th term : 11, 5, -1, -7,.........

Problem 8 :

12th 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? 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.

an  =  an-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, 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.

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.

an  =  an-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, -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.

Step 1 : Find the common difference.

2 - 6  =  -4

-2 - 2  =  -4

-6 - (-2)  =  -4

The common difference is -4.

Step 2 : Find the 25th term.

Write the rule to find the nth term.

an  =  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

Write the rule to find the nth term.

an  =  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

a16  =  83

Step 1 : Find the common difference.

5 - 11  =  -6

-1 - 5  =  -6

-7 - (-1)  =  -6

The common difference is -6.

Step 2 : Find the 60th term.

Write the rule to find the nth term.

an  =  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

Write the rule to find the nth term.

an  =  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

a12  =  19.6

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 20th term of the sequence, so n = 22.

Write the rule to find the nth term.

an  =  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

a22  =  61,440

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

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 6th term of the sequence, so n = 6.

Write the rule to find the nth term.

an  =  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. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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