MAC 1140 – Section 11.3 – Geometric Sequences and Series
A sequence in the form of a n  a1r n1 is known as a geometric sequence, where r is known as the common
rightterm
ratio. r =
, for each pair of successive terms.
leftterm
1. Identify the terms of the geometric sequence: an = 5(3)n-1
1<n< 4
2. Identify the first four terms of the geometric sequence: an = 2(-3)n-1
3. Identify the tenth term of the sequence: an  2(.03) n1
Working backwards. Write a formula for the nth term of the each geometric sequence.
4. 2, 4, 8, 16,…..
5. .7, .07, .007, .0007……
6. Write the geometric series in summation notation: 3 – 9 + 27 – 81 + 243 - 729
For 7 – 8, find the first four terms of each sequence. For 7-10, identify each sequence as arithmetic, geometric,
or neither. If arithmetic, identify common difference. If geometric, identify common ratio.
7. an = 3n
8. an = n + 5
9.
1 1
, ,1,4,...
6 3
10. 4, 1,
1 1
, ,...
4 16
Geometric Series – the sum of a geometric sequence – can be calculated using the following formulas:
Finite: Sum of first n terms:
a(1  r n )
Sn 
1 r
Infinite S n 
a
, where r  1
1 r
Find the sum of the geometric series.
11.
2 + 6 + 18 + 54 + 164
12. 1, 1/3, 1/9, 1/27, 1/81, 1/243

13.
 300(0.99)
i
(Note that this is a geometric series. Write the first few terms to confirm this. Determine
i 0
a1, r, and n then apply the formula)
14. 1 + ½ + ¼ + ……..
15. –4.4, 2.2, -1.1 ……

16.
 8(0.01)
i
i 0
(074)