LESSON 1

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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, t₈and t_n.

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 t_n.

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 t_n.

a = 2

r = 4

n = ?

t_n = 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 t_n

Solution:

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

Solution:

Example 5 :

Solution:

a = 16

r = ¼

n = 9, n