Arithmetic Sequence Review

Vocabulary

100

What does the "a₁" in the formula stand for?

The 1st term.

200

What does it mean when we say the "n^th" term?

What term are we trying to find?

300

What does the "d" in the formula stand for?

The common difference

400

How can you find the common difference?

By subtracting the 2nd term minus the 1st term

500

What is a sequence?

When you add (or subtract) the same amount each time to get the next number

Common Difference

100

Find the common difference of the following arithmetic sequence.

5, 10, 15, 20, .....

d = 5

200

Find the common difference of the following arithmetic sequence.

-7, -14, -21, -28, ...

d = -7

300

Find the common difference of the following arithmetic sequence.

175, 150, 125, 100, ...

d = -25

400

Find the common difference of the following arithmetic sequence.

6.5, 5, 3.5, 2, ...

d = -1.5

500

Find the common difference of the following arithmetic sequence.

-16, -7, 2, 11

d = 9

Find the missing term(s)

100

Find the missing term in the following Arithmetic sequence. 

3, ___ ,17, 24

10

200

Find the missing term in the following Arithmetic sequence. 

2, 16, _____ , 44

30

300

Find the missing term in the following Arithmetic sequence.

-6, -13, ___ ,-27

-20

400

Find the missing terms in the following Arithmetic sequence. 10, 14, _____ , _____, 26

18, 22

500

Find the missing terms in the following Arithmetic sequence.

 4, _____ , _____, 304

104 and 204

Find the nth term

100

Using the following arithmetic sequence, find the 16th term.

-14, -25, -36, -47, -58, ...... 

a16 = -179

200

Using the following arithmetic sequence, find a₇.

-100, -50, 0, 50,...

a₇ = 200

300

Using the following arithmetic sequence, find a₁₀.

 -16, -25, -34, -43, -52 

a₁₀ = -97

400

Using the following arithmetic sequence, find a₁₅.

 -3, -8, -13, -18, ....

a₁₅ = -73

500

Using the following arithmetic sequence, find a₅₀.

14, 11, 8, 5...

a₅₀ = -133

Explicit Formula

100

Write the explicit formula for the arithmetic sequence: 

*Hint use* : a_n = a₁ + d(n - 1)

2, 6, 10, 14, ...

a_{n = 2+ (4)(n-1)}

200

Write the explicit formula for the arithmetic sequence: 

*Hint use* : a_n = a₁ + d(n - 1)

-1, 2, 5, 8, 11

a_{n = -1 + (3)(n-1)}

300

Write the explicit formula for the arithmetic sequence: 

3, 9, 15, 21, ...

a_{n = 3 + (6)(n-1)}

400

Write the explicit formula for the arithmetic sequence: 

-16, -25, -34, -43, -52. 

a_{n = -16 + (-9)(n-1)}

500

Write the explicit formula for the arithmetic sequence: 

-100, -50, 0, 50,...

a_{n = -100 + (50)(n-1)}