Is the Sequence Arithmetic? Yes. Explanation: See solution. Recursive Formula: A(n)=A(n-1)+0.6, A(1)=0.3 Explicit Formula: A(n)=0.3+(n-1)(0.6)
Practice makes perfect
When a sequence is arithmetic, the difference between two consecutive terms is constant. Examining our sequence we can see that this is the case.
0.3 + 0.6 ⟶ 0.9 + 0.6 ⟶ 1.5 + 0.6 ⟶ 2.1 + 0.6 ⟶ ...
Since the difference between consecutive terms is constant and equal to 0.6, we have an arithmetic sequence with common difference 0.6. We will use this information to write both the recursive and the explicit formula.
Recursive Formula
Let's recall the general form of the recursive formula for an arithmetic sequence.
A(n)=A(n-1)+d
In the above formula, n is the term number and d the common difference. By substituting d= 0.6 into this formula, we can create our recursive rule.
To complete the recursive formula, we need to state the value of the first term, which in this case is A(1)= 0.3.
Recursive Formula
A(n)=A(n-1)+ 0.6, A(1)= 0.3
Explicit Formula
Now, let's recall the general form of an explicit formula.
A(n)=A(1)+(n-1)d
In the above formula, n, d, and A(1) are the term number, the common difference, and the first term, respectively. By substituting A(1)= 0.3 and d= 0.6 into this rule, we can create our explicit formula.
