Types of Sequences
Explain why the sequence 1, 3, 5, 7, . . . can be described as arithmetic.
Or the common difference (rate of change) is 2.
Write a recursive definition for the sequence f
23, 29, 35, 41, 47, . . .
1) f(1) = 23
2) f(n) = f(n-1) + 6
3) n >= 2
Write an explicit formula for the sequence h
3, -3, -9, . . .
h(n) = 3 - 6(n-1)
Find the sum of the first 20 terms of the sequence. Round to the nearest integer if necessary.
1, 1/2, 1/4, 1/8, 1/16
2
Mr. K is trying to get better at running. His first run lasts 10 minutes. Each subsequent week, his run will increase by 4 minutes.
Write the length of the first three runs.
10, 14, 18
Explain why the sequence 1, 1/2, 1/4, 1/8, 1/16 can be described as geometric.
To get the next term we multiply by the same constant (1/2).
Or the growth factor (common ratio) is 1/2.
Write a recursive definition for the sequence f
16, 24, 36, 54, 81, . . .
1) f(1) = 16
2) f(n) = 1.5f(n-1)
3) n>= 2
Write an explicit formula for the sequence k
96, 24, 6, . . .
k(n) = 96(1/4)n-1
Find the sum of the first 7 terms of the following sequence. Round to the nearest integer if necessary.
15, 10, 20/3
42
Mr. K is trying to get better at running. His first run lasts 10 minutes. Each subsequent week, his run will increase by 4 minutes.
Write a recursive definition to represent this sequence using function notation.
r(1) = 10
r(n) = r(n-1)+10
r(n) >= 2
Describe the sequence as arithmetic or geometric. Then find the common difference or common ratio.
1000, 933, 866, 799, 665, . . .
Arithmetic
common difference is -67
If f(1) = 2 and f(n) = 5f(n-1) then find the value of f(3).
f(3) = 50
Find the first three terms of the sequence given by the explicit equation
b(n) = 3 + 5(n-1)
3, 8, 13
Find the sum of the first 34 terms of the following sequence. Round to the nearest integer if necessary.
8, 12,16, . . .
2516
Mr. K is trying to get better at running. His first run lasts 10 minutes. Each subsequent week, his run will increase by 4 minutes.
Write an explicit definition for the length of Mr. K's runs.
r(n) = 10 +4(n-1)
Describe the sequence as arithmetic or geometric. Then find the common difference or common ratio.
-24, 16, -32/3, 64/9, . . .
Geometric
common ratio r = -2/3
Write the first three terms of the sequence g
g(1) = 6
g(n) = nf(n-1) - 3
n >= 2
6, 9, 24
Find the first 3 terms of the sequence given the explicit equation t(n)=-12*(1/2)n-1
-12, -6, -3
Find the sum of the first 29 terms of the following sequence. Round to the nearest integer if necessary.
28, 20, 12, . . .
f(n) = 28 - 8(n-1)
f(29) = 28 - 8(29-1) = -196
Sum = (29/2)(28 - 196) = -2436
Mr. K is trying to get better at running. His first run lasts 10 minutes. Each subsequent week, his run will increase by 4 minutes.
How many minutes will his run be in on the last week of the year? (1 year = 52 weeks)
k(n) = 10 + 4(n-1)
k(52) = 10 + 4(52-1)
k(52) = 214 minutes
Describe the sequence as arithmetic, geometric or neither. Explain how you know.
1, 4, 9, 16, 25, 36
If f(1) = 3 and f(n) = f(n-1)2 + n then find the value of f(3)
f(3) = 124
A sequence is defined by
f(0) = 4
f(n) = -3f(n-1)
n>=1
Write an explicit formula for f.
f(n) = 4(-3)n
The 3rd term of a geometric sequence is 20 and the 5th term is 320. Find the sum of the first 10 terms. Round to the nearest integer if necessary.
436906
Mr. K is trying to get better at running. His first run lasts 10 minutes. Each subsequent week, his run will increase by 4 minutes.
How many total minutes will he run in one year? (1 year = 52 weeks)
k(n) = 10 + 4(n-1)
k(52) = 214
Sum = (52/2)(10+214)= 5824 minutes