Intermediate Algebra (11th edition)

Determine the indicated term for each geometric sequence.

31.2, 32. , ;

Evaluate each sum if it exists.

33. 34. 35. 36.

12.4 Use the binomial theorem to expand each binomial.

37. 38. 39.

40.Write the fourth term of the expansion of 13 a+ 2 b 219.

12 p-q 25 1 x^2 + 3 y 24 13 t^3 - s^224

a

q

i= 1

a^2132 i

q

i= 1

4 a

1

5

b

i

a

8

i= 1

3

4

a^1 -^12 i

5

i= 1

a

1

4

b

i

• 6, 18,Á; a 11 a 3 = 20 a 5 = 80 a 10

710 CHAPTER 12 Sequences and Series

MIXED REVIEW EXERCISES

Determine the indicated term and evaluate for each sequence.

41. : geometric; 6, 42. : arithmetic; 1, 7, 13,


42. : arithmetic; , 44. : geometric; ,

Determine the general term for each arithmetic or geometric sequence.

45.2, 8, 32, 46.2, 7, 12,

47.12, 9, 6,Á 48.27, 9, 3,Á

Á Á

a 15 a 1 =- 4 d= 3 a 9 a 1 = 1 r=- 3

a 10 - 3, -12,Á a 40 Á

S 10

Solve each problem.

49.When Faith’s sled goes down the hill near her home, she covers 3 ft in the first second.

Then, for each second after that, she goes 4 ft more than in the preceding second. If

the distance she covers going down is 210 ft, how long does it take her to reach the

bottom?

50.An ordinary annuity is set up so that $672 is deposited at the end of each quarter for 7 yr.

The money earns 4.5% annual interest compounded quarterly. What is the future value

of the annuity?

51.The school population in Middleton has been dropping 3% per yr. The current popula-

tion is 50,000. If this trend continues, what will the population be in 6 yr?

52.A pump removes of the liquid in a container with each stroke. What fraction of the

liquid is left in the container after seven strokes?

53.Consider the repeating decimal number 0.55555.

(a)Write it as the sum of the terms of an infinite geometric sequence.

(b)What is rfor this sequence?

(c)Find this infinite sum if it exists, and write it as a common fraction in lowest

terms.

54.Can the sum of the terms of the infinite geometric sequence defined by be

found? Explain.

an= 5122 n

Á

1

2