The explicit rule of an arithmetic sequence combines the information provided by the two equations of the recursive rule into a single equation.
Recursive:& a_n=a_(n-1)+ d;
& a_1= a_1 [0.8em]
Explicit:& a_n= a_1+(n-1) dIn these rules, d is the common difference and a_1 is the first term. Looking at the given recursive rule, we can identify the common difference d and the value of the first term a_1.
a_1=5, a_n=a_(n-1)-1/3
⇕
a_1= 5, a_n=a_(n-1)+( - 1/3)
We can see that - 13 is the common difference and the first term is 5. Now we have enough information to form an explicit rule for this sequence.
