Description:
Sequence questions ask you to calculate a term in an arithmetic
sequence (addition), geometric sequence (multiplication), or unique sequence. Usually the
test makers will design their own sequence using a few mathematical rules.
Approach:
If the problem is arithmetic, find the difference D between consecutive
terms and use it to calculate later terms. If the problem is
geometric, find the ratio R between terms and use it to calculate later
terms. If the sequence is made up, create at least 3 new terms and look
for a pattern.
1) Arithmetic Sequences
In an arithmetic sequence, the difference between consecutive terms is
always the same. If the numbers in a sequence increase by D, you get the
next term by adding D.
Any term can be solved using the following equation:
tn = t1 + D(n - 1)
What is the fifth term of the following sequence: 5, 18, 31, 44 ...?
2) Geometric Sequence
In a geometric sequence, the ratio R between two consecutive terms is
always the same. In other words, if the numbers in a sequence
increase by a factor of R, you get the next term by multiplying by
R.
Any term can be solved using the following equation:
tn = t1
* R(n - 1)
What is the fifth term of the following sequence: -2, 6, -18, 54 ...?
3) Unique Sequences
A unique sequence will ask you to do some combination of addition,
subtraction, multiplication and division.
3 Steps to Solving a Unique Sequence
-
Add at least 3 more terms to the sequence
-
Break the sequence down into a repeating pattern
-
Apply the pattern to predict the desired term or terms
4) Practice:
-
What is the 10th term in the geometric series 2000, 1000, 500, 250 ...?
-
What is the 15 term in the arithmetic sequence 3, 7, 11, 15 ...?
-
The following sequence is formed by adding 2 to the first number to get
the second number, then multiplying by -1 to get the third number: -1,
1, -1 ...
This process repeats indefinitely; always add 2 to the odd
numbered terms of the set, and multiply the even numbered terms by -1.
What is the 27th term?
