Geometric Progressions
A geometric progression is a sequence in which the ratio of any two consecutive terms is the same. Thus, each term is generated by multiplying the preceding term by a fixed number.Example
What is the sixth term of the sequence 90, –30, 10, –10/3, . . . ?
- 1/3
- 0
- –10/27
- –3
- –100/3
Solution
Since the common ratio between any two consecutive terms is –1/3, the fifth term is
.
Hence, the sixth number in the sequence is .
The answer is (C).
Advanced concepts: (Sequence Formulas)
Note, none of the formulas in this section are necessary to answer questions about sequences on the GMAT.
Since each term of a geometric progression “is generated by multiplying the preceding term by a fixed number,” we get the following:
first term | a | |
second term | where r is the common ratio | |
third term | ||
fourth term | ||
. . . | ||
nth term | This formula generates the nth term |
The sum of the first n terms of an geometric sequence is