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