Mental Math: The next term of a sequence 5, 6, 7, 9, 12, 17 ... is _______.  

Expert Answers
jgeertz eNotes educator| Certified Educator

Sequences are a set of numbers in order. There are many different types of sequences. Sometimes a constant is added to find the next number in a sequence; sometimes each number is squared to determine the next number in a sequence, and so on.

The next term in the sequence above

5,6,7,9,12,17, ....

is a bit more complicated.

It is a type of Fibonacci sequence and follows the formula

a_n= 1/2( F_n + L_n +8)   

where F_n  is the nth Fibonacci number and L_n  is the nth Lucas number.


Therefore the next term in the sequence would be 25.