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UNIT 10  :  SEQUENCES AND SERIES

LESSON 4: GEOMETRIC SERIES HOMEWORK QUESTIONS

Quick Review:

Geometric Series:

Recall a sequence such as  2, 4, 8, 16, 32,   is called a Geometric Sequence.  These sequences have the following properties.

·        Terms are denoted as t1 , t2 , t3 , referring  to term1, term 2, term 3

·

·        This ratio is called the common ratio and denoted using the letter r.  Here r = 2.

·        The first term is denoted using the letter a.  Here a = 2.

·        Successive terms are found by multiplying a given term by the common ratio.  Eg.   t6 = 32 x 2 = 64 etc.

·        The formula for the general term or nth term is   tn = arn-1.

·        Geometric sequences are exponential functions with domain the natural numbers N = {1, 2, 3, 4, }

Definition: The sum of the terms of a Geometric sequence is a Geometric Series.

Homework Questions:

1.  In each of the following geometric series, determine S9 , unless otherwise specified .

a)  3 + 6 + 12 +

b)  7  14  + 28  56 +

c)  2 + 10 + 50 +

[to five terms only]

[to eight terms only]

2.  Find the sum of the following geometric series.

3.  Last year InternetCorp had gross revenue of \$500 000.  If revenue increases by 15% per year, find the total revenue achieved by the company after 5 years.

4.  A certain geometric series has t1 = -2 and t5 = -32.  Find S12.

5.  A certain geometric series has r = -3 and S8 = -3280.  Find a.

6.  A certain geometric series has t3 = 12 and t8 = 384.  Find S11.

Solutions:

1.  In each of the following geometric series, determine S9 , unless otherwise specified .

a)  3 + 6 + 12 +

b)  7  14  + 28  56 +

c)  2 + 10 + 50 +

[to five terms only]

[to eight terms only]

Solutions:

 a = 3 r = 2 n = 9 S9 = ?

 a = 7 r = -2 n = 9 S9 = ?

 a = 2 r = 5 n = 9 S9 = ?

 a = 64 n = 5 S5 = ?

 a = 2 d = 0.5 n = 60 Sn = ?

2.  Find the sum of the following geometric series.

Solutions:

 a = 4 r = 2 n = ? tn = 1024 Sn = ?

 a = -2 r = 3     n = ? tn = - 4374 Sn = ?

3.  Last year InternetCorp had gross revenue of \$500 000.  If revenue increases by 15% per year, find the total revenue achieved by the company after 5 years.

Solution:

The company maintains 100% of its previous years revenue and gains 15% more.  Therefore to get the next years revenue, multiply the previous years revenue by 115% (1.15 in decimal form).

4.  A certain geometric series has t1 = -2 and t5 = -32.  Find S12.

Solution:

5.  A certain geometric series has r = -3 and S8 = -3280.  Find a.

Solution:

6.  A certain geometric series has t3 = 12 and t8 = 384.  Find S11.

Solution: