Equations & Inequalities - Algebra 1



Name: __________________________________________________________ Date: ____________________________

Arithmetic Sequences Classwork Worksheet

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Arithmetic Sequences: A sequence of terms that have a common _____________________ between them.

Explicit Formula: An = a1 + d(n-1) where a1 is the first number in the sequence and d is the common difference.

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Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms.

1. 6, 12, 18, 24, … d: ________ Next three terms: ____________________________

2. 6, 11, 17, … d: ________ Next three terms: ____________________________

3. 2, 14, 98, 686, … d: ________ Next three terms: ____________________________

4. 160, 80, 40, 20, … d: ________ Next three terms: ____________________________

5. -40, -25, -10, 5, … d: ________ Next three terms: ____________________________

6. 7, -21, 63, -189, … d: ________ Next three terms: ____________________________

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For the following sequences, find a1 and d and state recursive formula for the sequence.

7. -10, -4, 2, 8, 14, … a1 = __________ d = __________ Formula:

8. 10, 8, 6, 4, … a1 = __________ d = __________ Formula:

9. 36, 31, 26, 21, … a1 = __________ d = __________ Formula:

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Find the indicated term of each arithmetic sequence.

Use the Explicit Formula to find the specified term; DON’T FORGET TO SIMPLIFY THE EXPLICT FORMULA

10. 0, -0.25, -0.5, -0.75, … a17 = __________

11. 51st term: a1 = 7; d = -4.7

12. 2, 5/2, 3, 7/2, … a99 = __________

13. 46th term: a1 = 46; d = 46

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THIS IS HOW THE PROBLEMS LOOK ON YOUR CDA LOOK SO YOU CANNOT SKIP THIS SIDE!

PLEASE ATTEMPT EACH PROBLEM.

1) Create a table if you can so you can see the pattern

2) Write the explicit formula plug in in a1, d, and n (term you trying to find)

3) Answer the question posed in the problem using a sentence.

14. Fred decides to cover the kitchen floor with tiles of different colors. He starts with a row of four tiles of the same color. He surrounds these four tiles with a border of tiles of a different color (Border1). The design continues as shown below:

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How many tiles will there be for Border 10 (make a chart to find the pattern)?

15. Paul has $680 in a savings account. He makes a deposit after he receives each paycheck. After one month he has $758 in the account. The next month the balance is $836. The balance after the third month is $914. How much money will he have in his account after 16 months?

16. The table shows the number of country club members for four years after it began. How many members will there be in 20 years?

|Time(yrs) |1 |2 |3 |4 |

|Members |200 |300 |400 |500 |

17. A photographer charges a sitting fee of $69.95 for one person. Each additional person in the picture is $30. What is the total sitting fee charge if a group of 10 people wish to be photographed?

18. Grant is planting one large tree and several smaller trees. He has a budget of $1400. A large tree costs $200. Each smaller tree is $150. How many total trees can Grant purchase on his budget?

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