Arithmetic Sequences

sequence

number pattern

arithmetic sequence

a numerical pattern that adds or subtracts at a constant rate or value

term

Each number in the sequence (y) or f(x)

consecutive terms

a term directly after another term

common difference

the difference between any two consecutive terms in an arithmetic sequence

Find the common difference:

16, 25, 34, ..

9

Find the common difference in the sequence: 10, 3, -4, -11, ...

-7

Find the next three terms in the sequence: 3, 7, 11, 15, ...

19, 23, 27

Find the next three terms in the sequence: 4, -1, -6, ...

-11, -16, -21

What is the Formula Rule of an arithmetic sequence? What does each term mean?

A(𝑛) = a₁+ d(𝑛-1)

𝑛 = the term number in the sequence

A(𝑛)=value of the nth term of the sequence

Find the 10th term in the sequence: -5, -2, 1, 4, ...

22

Find the nth term in the sequence. (Write the explicit formula): 10, 12, 14, 16, ...

2n + 8

Find the nth term (Write the explicit formula): -12, -2, 8, 18, ...

10n - 22

Find the 21st term in the sequence.

-4, 1, 6, 11, 16, ...

96

Find the 72nd term in the sequence:

-5, -1, 3, 7, ..

279

Find the first term in a sequence where the common difference is 6 and the eleventh term is 77.

17

Find the 12th term in a sequence with common difference -8 and first term 58.

-30

Find the first, second, fifth, and ninth terms of the sequence.

A(𝑛) = -9 + (𝑛-1)6

Write the first five terms of the sequence, explain what the fifth term means in context to the situation.

A baby's birth weight is 7 lbs. 4 oz., the baby gains 5 oz. each week.

Write the first five terms of the sequence, explain what the fifth term means in context to the situation.

The balance of a car loan starts at $4,500 and decreases $150 each month.

Find the second, fourth, and eighth terms of the sequence.

A(𝑛) = 1/5 + (𝑛 - 1)4/5

Is the pattern an arithmetic sequence? Why?

2, 5, 8, 11, _______, _______

Yes, each number is the previous number plus 3

Is the pattern an arithmetic sequence? Why?

2, 4, 8, 16, _______, _______

No, each number is the previous number multiplied by 2

Is the pattern an arithmetic sequence? Why?

1, 4, 9, 16, _______, _______

No, each term is the square of the next consecutive integer, starting with 1.

Is the pattern an arithmetic sequence? Why?

3, 9, 27, 81, _______, _______

No, each term is the previous number multiplied by 3

Is the pattern an arithmetic sequence? Why?

9, 15, 21, 27, _______, _______

Yes, each term is the previous number plus 6

Is the pattern an arithmetic sequence? Why?

2, -4, 8, -16, _______, _______

No, each term is the previous number multiplied by -2.