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_1= a_1; a_n=a_(n-1) + d
Explicit:& a_n= a_1 + (n-1) d
In these formulas, d is the common difference and a_1 is the first term.
Looking at the given explicit formula, we cannot identify the common difference d nor the value of the first term a_1. So let's rewrite the formula.
Now we can identify the common difference d and the value of the first term a_1.
a_n= 4.5 + 1.5(n-1)
We can see that 1.5 is the common difference and the first term is 4.5. Now we have enough information to form a recursive formula for this sequence.
la_1 = a_1 a_n = a_(n-1) + d ⇒ la_1 = 4.5 a_n = a_(n-1) + 1.5
