Let’s do another symbolism question with two symbols:If the operation # is defined for all numbers, a and b, by a # b = √ab, then
60 # (25 # 9) =?
Step 1: Understand the formula: multiply the terms before and after the
symbol and then take their square root.
Step 2: Since 60 # (25 # 9) is a compound function, you should first find
the value of (25 # 9) and then input that value into the original function:
25 # 9 = √25 × 9 = 15.
Step 3: Solve for 60 # 15: √60 × 15 = √ 900 = 30.Sequences
The last type of formula question you will see are sequences. A sequence is any
group of numbers whose order is determined by a rule. Consecutive integers are
an example of a sequence: for example, the rule for the set of consecutive integers
3, 4, 5, 6, 7 is that any given term in the set is one more than the term before it.
Mathematically, the previous sequence would be defined in the following way:
an = an−1 + 1, where n > 1
The subnotation refers to the position of a term in the sequence. So a 1 is the first
term of the sequence, a 2 is the second term, and so on. The rule tells you that
the nth term of the sequence equals the value of previous term plus 1. Why does it
specify “where n > 1”? Because this rule cannot apply to the first term, since there is
no number preceding that term. Thus starting with the second term, any term will
have a value one greater than the term before it.
Generally, sequence questions will ask you to determine one of three things:- The rule for a series of numbers
- The value of a specific term in the sequence
- The sum or difference of two or more terms in the sequence
Example 1: The sequence a 1 , a 2 , a 3 ,... , an,... is such that an = 2an−1 for all
n > 1. If a 2 = 7, what is a 5?SOLUTION: The rule is that any given term is double the term before it. a 5 is
3 places after a 2 , so
a 5 = a 2 × 2 × 2 × 2
a 5 = 8a 2
Since a 2 = 7, you know that a 5 = 8 × 7 = 56.294 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 294 12/05/17 11:55 am