Arithmetic/Geometric
The explicit equation for a geometric sequence with a first term of a_1 = 2 and a common ratio of r = 3.
a(n) = 2(3)^n-1
A movie theater starts with 8 workers and hires 2 new workers each week. This is the common difference.
2
Choose the correct equation for an arithmetic sequence in which t(3) = 11 and t(7) = 27.
a) t(n) = 3n + 2
b) t(n) = 4n - 1
c) t(n) = 5n - 4
d) t(n) = 2n + 5
b) t(n) = 4n - 1
The slope of the line that passes through the points (4, 1) and (6, 5).
m = 2
3x + 8 = 23
5
The explicit equation for an arithmetic sequence where the first term is a_1 = 15 and the common difference is d = 5.
a(n) = 5n + 10
The explicit equation for a sequence where a writer starts with 50 pages and writes 7 pages per day.
a(n) = 7n + 43
Choose the correct equation for an arithmetic sequence in which t(1) = 8 and t(5) = 20.
a) t(n) = 2n + 6
b) t(n) = 3n + 5
c) t(n) = 4n + 4
d) t(n) = 5n + 3
b) t(n) = 3n + 5
The equation of a line with a slope m = -3 and a (4,5)
y = -3x + 17
x/4 - 7 = -3
16
The 10th term in the sequence defined by the explicit equation a(n) = 11 + 3(n-1).
38
The number of trees planted on the 8th day if 12 trees are planted on the first day and the number increases by 5 each day.
47 trees
Choose the correct equation for an arithmetic sequence in which t(4) = 17 and t(9) = 42.
a) t(n) = 5n - 3
b) t(n) = 6n - 7
c) t(n) = 4n + 1
d) t(n) = 7n - 11
a) t(n) = 5n - 3
The equation of the line that passes through (1, 4) is with a slope m = 5.
y = 5x - 1
5^(2x) = 625
2
The explicit equation for the arithmetic sequence 10, 22, 34, 46, ....
a(n) = 12n - 2
The session number when a swimmer, who starts at 15 laps and increases by 3 laps per session, swims 36 laps.
8 (or 8th session)
Choose the correct equation for an arithmetic sequence in which t(2) = -3 and t(8) = 15.
a) t(n) = 2n - 7
b) t(n) = 3n - 9
c) t(n) = 4n - 11
d) t(n) = 5n - 13
b) t(n) = 3n - 9
The equation of the line that passes through (0, 9) and (2, 1).
y = -4x + 9
6^(x+3) = 36^(x-1)
5
The explicit equation for the geometric sequence 81, 27, 9, 3, ...
a(n) = 81(1/3)^n-1
The explicit equation that models the cost of a rental car if the initial fee is $35 and the daily fee is $45.
C(d) = 45d + 35
Choose the correct equation for an arithmetic sequence in which t(5) = 23 and t(12) = 58.
a) t(n) = 4n + 3
b) t(n) = 6n - 7
c) t(n) = 5n - 2
d) t(n) = 7n - 12
c) t(n) = 5n - 2
The equation of the line that passes through (-4, -2) and (1, 8).
y = 2x + 6
4^(x-1) = 8^(2x+3)
-7