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Arithmetic Sequences

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 UNIT 10 : SEQUENCES AND SERIES

 LESSON 2: GEOMETRIC SEQUENCES

 

 

Text Box: a = t1 = first term
r = common ratio
n = term number
 

 

 

 

 

 

 

 


Example 1:

Form the geometric sequence determined by the exponential function f(n) = 3(2)n-1. Find a, r, t8 and tn.

Solution:

 

 

 

Example 2: Finding specific terms and the General (nth) Term.

Given the sequence 2, -6, -18, -54 ,

a) Show that the sequence is geometric.

b) Find t7, t11 and the general term tn.

 

Solution:

 

a = - 2

r = 3

n = 7, 11, n

 

 

 

 

 

 

 

 

Example 3: Finding the Number of Terms in a Given Sequence.

Given the sequence 2, 8, 32, , 32768. Find the number of terms in the sequence.

Solution:

Let the last term be tn.

a = 2

r = 4

n = ?

tn = 32768

 

 

 

 

 

 

 

 

 

 

 

 

Example 4: Solving a Sequence given two terms.

a) The first and sixth terms of a geometric sequence are 5 and 160 respectively. Find a, r and tn

Solution:

b) The fourth and eighth terms of a geometric sequence are 2 and 162 respectively. Find a, r and tn.

Solution:

 

Example 5 :

Solution:

 

 

 

 

a = 16

r =

n = 9, n

 
 

 

 

 

 

 

 


 

 

 

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