The explicit formula of an arithmetic sequence combines the information provided by the two equations of the recursive form 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 formulas, d is the common difference and A(1) is the first term.
Looking at the given recursive formula, we can identify the common difference d and the value of the first term A_1.
A(n)=A(n-1)+ 3; A(1)= 4
We can see that 3 is the common difference and the first term is 4. Now we have enough information to form an explicit formula for this sequence.
