Number and Operations
Sequences
Two common types of sequences that appear on the SAT are arithmetic and geometric sequences.
An arithmetic sequence is a sequence in which successive terms differ by the same constant amount.
For example: 3, 5, 7, 9, . . . is an arithmetic sequence.
A geometric sequence is a sequence in which the ratio of successive terms is a constant.
For example: 2, 4, 8, 16, . . . is a geometric sequence.
A sequence may also be defined using previously defined terms. For example, the first term of a sequence is 2, and each successive term is 1 less than twice the preceding term. This sequence would be 2, 3, 5, 9, 17, . . .
On the SAT, explicit rules are given for each sequence. For example, in the sequence above, you would not be expected to know that the 6th term is 33 without being given the fact that each term is 1 less than twice the preceding term. For sequences on the SAT, the first term is never referred to as the zeroth term.
