7.06

1. find the first six terms of the sequence.
a1 = -7, an = 4 • an-1

a) -7, -28, -112, -448, -1792, -7168
b) -28, -112, -448, -1792, -7168, -28,672
c) -7, -28, -24, -20, -16, -12
d) 0, 4, -28, -24, -20, -16

2. find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2,

an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)

3. find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5

a) an = -725 - 48(n - 1)
b) an = -725 + 48(n + 1)
c) an = -725 + 48(n - 1)
d) an = -725 - 48(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.
-4, -16, -64, -256,

a) an = 4 • -4n
b) an = 4 • -4n + 1
c) an = -4 • 4n
d) an = -4 • 4n - 1

6. find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

a) an = 1 • (-2)n - 1
b) an = 1 • 2n
c) an = 1 • (-2)n + 1
d) an = 1 • 2n - 1

7. write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 +

a) summation of four times six to the power of n from n equals zero to infinity
b) summation of four times negative six to the power of n from n equals zero to infinity
c) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
d) summation of four times six to the power of the quantity n plus one from n equals zero to infinity

8. write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + + 132

a) summation of negative 27 times n from n equals 0 to infinity
b) summation of negative 27 times n from n equals 0 to 15
c) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
d) summation of the quantity negative 3 plus 9 n from n equals 0 to 15

9. write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + + n3

a) summation of the quantity n minus 1 cubed from n equals 7 to infinity
b) summation of n cubed from n equals 7 to infinity
c) summation of n cubed from n equals 8 to infinity
d) summation of the quantity n plus 1 cubed from n equals 7 to infinity

10. find the sum of the arithmetic sequence.
3, 5, 7, 9, 21

a) 39
b) 120
c) 20
d) 23

11. find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

a) 1363 divided by 3
b) 1364 divided by 15
c) 1364 divided by 3
d) 1363 divided by 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.
10 + 20 + 30 + + 10n = 5n(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.