Arithmetic Sequences, Geometric Sequences
sequence
number pattern
common difference
the difference between any two consecutive terms in an arithmetic sequence
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
Find the nth term (Write the explicit formula): -12, -2, 8, 18, ...
10n - 22
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
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..
1/4
What is the common ratio? 64, 16, 4 , 1...
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
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
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.
Geometric
Determine if the sequence is arithmetic, geometric or neither: 100, 50, 25, 12.5
1/5
Determine the common ration: 500, 100, 20
125
Find f(1) for the sequence: 125, 25, 5...
54
Find f(3) for the given sequence: 6, 18, 54...