Math Help
1)Find the first six terms of the sequence.
a1 = -1, an = 2 • an-1
a) -2, -4, -8, -16, -32, -64
b) -1, -2, -4, -8, -16, -32
c) -1, -2, 0, 2, 4, 6
d) 0, 2, -2, 0, 2, 4
2)Find an equation for the nth term of the arithmetic sequence.
-17, -14, -11, -8, ...
a) an = -17 + 3(n - 1)
b) an = -17 x 3(n - 1)
c) an = -17 + 3(n + 1)
d) an = -17 + 3(n + 2)
3)Find an equation for the nth term of the arithmetic sequence.
a19 = -92, a20 = 6
a) an = -1856 + 98(n - 1)
b) an = -1856 - 98(n - 1)
c) an = -1856 - 98(n + 1)
d) an = -1856 + 98(n + 1)
4)Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
a) Diverges
b) Converges; 231
c) Converges; 3751
d) Converges; 935
5)Find an equation for the nth term of the sequence.
-2, -8, -32, -128, ...
a) an = 4 • -2n
b) an = -2 • 4n - 1
c) an = -2 • 4n
d) an = 4 • -2n + 1
6)Find an equation for the nth term of a geometric sequence where the second and fifth terms are -8 and 512, respectively.
a) an = 2 • (-4)n + 1
b) an = 2 • 4n - 1
c) an = 2 • (-4)n - 1
d) an = 2 • 4n
7)Write the sum using summation notation, assuming the suggested pattern continues.
2 - 12 + 72 - 432 + ...
a)
b)
c)
d)
8)Write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + ... + 132
a)
b)
c)
d)
9)Write the sum using summation notation, assuming the suggested pattern continues.
8 + 27 + 64 + 125 + ... + n3
a)
b)
c)
d)
10)Find the sum of the arithmetic sequence.
5, 7, 9, 11, ..., 23
a) 59
b) 40
c) 25
d) 140
11)Find the sum of the geometric sequence.
a)31/3
b)10
c)2
d)31/15
12)An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
a) 390
b) 580
c) 620
d)400
13)Use mathematical induction to prove the statement is true for all positive integers n.
8 + 16 + 24 + ... + 8n = 4n(n + 1)
14) A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.