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UNIT
8 :
SEQUENCES AND SERIES
LESSON 2:
GEOMETRIC SEQUENCES
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 = ¼ n = 9, n