     Home Arithmetic Sequences Geometric Sequences Arithmetic Series Geometric Series Sigma Notation Mathematical Induction Review&Test UNIT 10  :  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 