Sums of a Finite and Infinite Geometric Sequences

1

1( )1

n

n

rS a

r

1

1

aS

r

Homework from 3/23

71.

73.

75.

500

1

( 3)n

n

20

1

(2 5)n

n

50

0

(1000 5 )n

n

77.

79. Find the sum of the first 100 positive odd integers.

60

1

8(250 )

3i

i

81. Consider a job offer with the given starting salary and guaranteed salary increase for the first 5 years of

employment.

(a) Determine the person’s salary during the sixth year of employment.

(b) Determine the person’s total compensation from the company through 6 full years of employment.

Starting Salary Annual Raise

$32,500 $1500

83. Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 24 seats in the second row,

28 seats in the third row, and so on.

85. A brick patio has the approximate shape of a trapezoid, as shown in the figure. The patio has 18 rows of bricks. The first row has 14 bricks and the 18th row has 31 bricks. How many bricks are in the

patio?

87. Each row in a small auditorium has two more seats than the preceding row, as shown in the figure. Find the seating capacity of the auditorium if the front seats 25 people and there are 15 rows of seats.

89. Each hour, a grandfather clock strikes the number of times corresponding to the hour of the day. How many

times does the clock strike in a day?

Sum of a finite geometric sequence

1

1( )1

n

n

rS a

r

Sum of an infinite geometric sequence

1

1

aS

r

Find the sum:

12

1

4(0.3)n

n

Find the sum

1

1

4(0.6)n

n

Find the sum

• 3+0.3+0.03+0.003+…

A deposit of $50 is made on the first day of each month in a savings account that pays 6% compounded monthly. What is the balance of

this annuity at the end of 2 years?

Homework: p. 644 (61,63,75,77,81,89,91)

*Hint: on #91, write out a few years and determine r.