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=3, a_n=a_(n-1)-6
⇕
a_1= 3, a_n=a_(n-1)+( - 6)
We can see that - 6 is the common difference and the first term is 3. Now we have enough information to form an explicit rule for this sequence.
