Arithmetic Sequences, Geometric Sequences

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

-11, -16, -21

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

-30

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

-7

Simplify the following arithmetic sequence explicit formulas 1. A(𝑛) = -9 + (𝑛-1)6 2. A(𝑛) = 1/5 + (𝑛 - 1)4/5

1. A(𝑛) = 6𝑛 - 15 2. A(𝑛) = 4/5𝑛 - 3/5

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

10n - 22

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

17

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

19, 23, 27

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

22

Find the 72nd term in the sequence: -5, -1, 3, 7, ..

279

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

2n + 8

Find the common difference: 16, 25, 34, ..

9

Find the 21st term in the sequence. -4, 1, 6, 11, 16, ...

96

What is the Explicit Formula/Function Rule of an arithmetic sequence? And, what does each variable represent?

A(𝑛) = a₁+ d(𝑛-1) 𝑛 = the term number in the sequence (input/x) A(𝑛)=value of the nth term of the sequence(output/f(x)/y)

Geometric

Determine if the sequence is arithmetic, geometric or neither: 100, 50, 25, 12.5

1/5

Determine the common ration: 500, 100, 20

term

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

125

Find f(1) for the sequence: 125, 25, 5...

54

Find f(3) for the given sequence: 6, 18, 54...

486

Find f(6) for the given sequence: 2, 6, 18...

(1/5)

Find the common ratio of the sequence: 1/4, 1/20, 1/100

3

Find the common ratio of the sequence: 4, 12, 36

(1/3)

Find the common ratio of the sequence: 81, 27, 9

4

Find the common ratio: 1, 4, 16, 64

t(n) = 48(1/2)ⁿ⁻¹

Find the equation of the sequence: 48, 24, 12, 6, 3

f(n)=1(4)ⁿ⁻¹

Find the explicit rule for the sequence: 1, 4, 16...

f(n)=125(1/5)ⁿ⁻¹

Find the explicit rule for the sequence: 125, 25, 5...

1, -4, 16, -64, 256

Find the first five terms of the sequence: t(n) = 1(-4)ⁿ⁻¹

243, 729

Find the next 2 numbers 3, 9, 27, 81

-192, 768, -3072

Find the next three terms of the sequence: 3, -12, 48

Term number: 1 2 3 4 ← input Term: 7 11 15 19 ←output

Function Rule/Explicit Formula: A(𝑛) = 7 + 4(𝑛-1) Simplified: A(𝑛) = 4n +3 Input Output 𝑛 A(𝑛) 1 7 7 + 0 (4) 7 2 7 + 4 7 + 1 (4) 11 3 7 + 4 + 4 7 + 2 (4) 15 4 19

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

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

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? 1, 4, 9, 16, _______, _______

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

Arithmetic Means

The missing terms in an arithmetic sequence.

term number

The order number in which the term falls in the sequence (x)

18,54,162

What are the three missing terms? 6__,__,__486

10,20

What are the two missing terms? 5,__,__40

3

What is the common ratio? 2, 6, 18, 54..

2

What is the common ratio? 5,__,__40

1/4

What is the common ratio? 64, 16, 4 , 1...

3

What is the common ratio? 6__,__,__486

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? 9, 15, 21, 27, _______, _______

Yes, each term is the previous number plus 6

arithmetic sequence

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

consecutive terms

a term directly after another term

sequence

number pattern

common difference

the difference between any two consecutive terms in an arithmetic sequence