Arithmetic Sequences Grade 12
Find the next three terms in the sequence: 4, -1, -6, ...
-11, -16, -21
Find the next three terms of the sequence: 305, 225, 145, 65,
-15, -95, -175
Find the 12th term in a sequence with common difference -8 and first term 58.
-30
-31 is what term of the sequence: 98, 95, 92, 89...
-31 is the 44th term
Find the 21st term in the sequence. -4, 1, 6, 11, 16, ...
-4 + (21-1)(5) -4 + 20 x 5 -4 + 100 = 96
Find the 81st term of the sequence: 4,-2, -8, -14,...
-476
Find the common difference in the sequence: 10, 3, -4, -11, ...
-7
Find the next three terms of the sequence: -39, -31, -23, -15,
-7, 1, 9
What are the missing numbers? -4,__,__,__-16
-7,-10,-13
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 nth term: -12, -2, 8, 18, ...
10n - 22
What are the missing numbers? 8,__,__,29
15,22
Find the 21st term of the arithmetic sequence: 72, 76, 80, 84,...
152
Find the 52nd term of the sequence: 7, 10, 13, 16, ...
160
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
197 is what term of the sequence: 53, 59, 65, 71,...
197 is the 25th term
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
What is the common difference? 8,__,__,29
7
Find the 21st term of the arithmetic sequence: 57, 44, 31, 18,...
78
Find the common difference: 16, 25, 34, ..
9
What type of equation is an arithmetic sequence most similar?
A linear equation
Arithmetic Sequence
A sequence in which the difference between terms is constant.
What is the Rule of an arithmetic sequence? And, what does each variable represent?
A(𝑛) = a₁+ d(𝑛-1) 𝑛 = the term number in the sequence A(𝑛)=value of the nth term of the sequence
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)
What is the pattern for this sequence? 2, 5, 8, 11, _______, _______
ADD 3
Sequence
An ordered list of numbers.
Explicit Formula
Describes any term in the sequence using the term number.
term
Each number in the sequence
term
Each number in the sequence (y) or f(x)
What is the Explicit Formula/Function Rule of an arithmetic sequence? And, what does each variable represent(m and b)?
F(x) = mx + b m is the common difference b is the zero term
22
Find the 10th term in the sequence: -5, -2, 1, 4, ...
-30
Find the 12th term in a sequence with common difference -8 and first term 58.
96
Find the 21st term in the sequence. -4, 1, 6, 11, 16, ...
279
Find the 72nd term in the sequence: -5, -1, 3, 7, ..
-7
Find the common difference in the sequence: 10, 3, -4, -11, ...
9
Find the common difference: 16, 25, 34, ..
17
Find the first term in a sequence where the common difference is 6 and the eleventh term is 77.
19, 23, 27
Find the next three terms in the sequence: 3, 7, 11, 15, ...
-11, -16, -21
Find the next three terms in the sequence: 4, -1, -6, ...
39
Find the ninth term in the sequence with the given explicit rule: a(n) = -9 + (n-1)6
a(n) = 10n - 22
Find the nth term (Write the explicit formula): -12, -2, 8, 18, ...
a(n) = 2n + 8
Find the nth term in the sequence. (Write the explicit formula): 10, 12, 14, 16, ...
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
First Five Terms: 15/8, 19/8, 23/8, 27/8, 31/8
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: 28, 38, 48, 58, 68
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: 35, 39, 43, 47, 51
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: −34, −44, −54, −64, −74
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: −35, −135, −235, −335, −435
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: −38, −138, −238, −338, −438
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: −4, 3, 10, 17, 24
Given the explicit formula for an arithmetic sequence find the first 5 terms.
First Five Terms: −9.2, −11.3, −13.4, −15.5, −17.6
Given the explicit formula for an arithmetic sequence find the first 5 terms.
No, each term is the square of the next consecutive integer, starting with 1.
Is the pattern an arithmetic sequence? Why? 1, 4, 9, 16, _______, _______
No, each term is the previous number multiplied by -2.
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, _______, _______
Yes, each number is the previous number plus 3
Is the pattern an arithmetic sequence? Why? 2, 5, 8, 11, _______, _______
No, each term is the previous number multiplied by 3
Is the pattern an arithmetic sequence? Why? 3, 9, 27, 81, _______, _______
Yes, each term is the previous number plus 6
Is the pattern an arithmetic sequence? Why? 9, 15, 21, 27, _______, _______
What is the pattern for this sequence? 3, 9, 27, 81, _______, _______
MULTIPLY by 3
Find the common difference: 1/3, 1/4, 1/5, 1/6,...
No common difference
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.
Find the 30th term of 1, 3, 5, 7, ... .
The 30th term is 59.
Common Difference
The difference between consecutive terms in an arithmetic sequence.
Arithmetic Means
The missing terms in an arithmetic sequence.
Terms
The numbers in a sequence.
term number
The order number in which the term falls in the sequence (x)
Tenth term of the following sequence is? 3, 5, 7, 9, ...
The tenth term is 21.
Common Difference
The term that is added to the previous term in an arithmetic sequence to get to the next term.
a(n) = 2n - 19
What is the explicit rule for an arithmetic sequence that has a(14) = 9 and a common difference of 2.
a(n) = a(n-1) + 6
What's the recursive rule for the following arithmetic sequence? -11, -5, 7, 13...
a(n) = a(n-1) -15
What's the recursive rule for the following arithmetic sequence? 40, 25, 10, -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? 9, 15, 21, 27, _______, _______
Yes, each term is the previous number plus 6
Find the explicit formula for the following sequence. 1, 3, 5, 7, ...
a = 2n - 1.
arithmetic sequence
a numerical pattern that adds or subtracts at a constant rate or value
consecutive terms
a term directly after another term
a numerical pattern that adds or subtracts at a constant rate or value
arithmetic sequence
the difference between any two consecutive terms in an arithmetic sequence
common difference
a term directly after another term
consecutive terms
Common Difference
d The difference between 2 consecutive terms in a sequence
What is the common difference of 15, 10, 5, 0, -5, -10, ...?
d = -5
What is the common difference of 1, 4, 7, 10, 13, 16, ...?
d = 3
What is the common difference for the arithmetic sequence whose explicit formula is a = 6n + 3?
d = 6.
Write the recursive formula for 2, 8, 14, 20...
f(1)=2; f(x)=f(x-1) +6
Write the recursive formula for 3, -4, -11, -18...
f(1)=3; f(x)=f(x-1) -7
Function notation for an arithmetic sequence
f(n) = f(1) + d(n-1)
Find the nth term (Write the explicit formula): -12, -2, 8, 18, ...
f(x)=10x - 22
Find the nth term in the sequence. (Write the explicit formula): 10, 12, 14, 16, ...
f(x)=2x + 8
term number
n the location or x-value of any number in a sequence
number pattern
sequence
Initial Value
t1 The first term in a sequence
Each number in the sequence
term
common difference
the difference between any two consecutive terms in an arithmetic sequence
nth term
tn any term
function formula (explicit)
tn = t1 +d(n-1) the equation used to find any term in the sequence
recursion formula
tn = tn-1 +d used to find the next term by applying the common difference to the previous term
What is the common difference? -4,__,__,__-16
-3
Find the 100th term of the arithmetic sequence: 1, 51, 101, 151,...
4951
Find the 21st term in the sequence. -4, 1, 6, 11, 16, ...
96
What is the pattern for this sequence? 2, 4, 8, 16, _______, _______
MULTIPLY by 2
sequence
number pattern
