Choose an arbitrary value for the common difference and use it to find the value of the fifth term. Use a similar procedure to find the rest of the terms.
Since we do not have any restrictions for the common difference, we can arbitrarily choose any value. Let the common difference be d= 4. Knowing the sixth term and the common difference, we can find the fifth term. To do so, we subtract the common difference from the value of the sixth term.
A(5)= 25- 4 ⇔ A(5)= 21
In a similar way, we can find A(4), A(3), A(2), and A(1).
A(4)= 21- 4 &⇔ A(4)= 17
A(3)= 17- 4 &⇔ A(3)= 13
A(2)= 13- 4 &⇔ A(2)=9
A(1)= 9- 4 &⇔ A(1)= 5
With this information, we can complete our table.
Now we can use the explicit formula for an arithmetic sequence to write a function rule for our sequence.
A(n) = A(1) + (n-1) d
In this formula, A(1) is the first term and d is the common difference. The first term of our sequence is 5, and the common difference is 4. We can substitute these values into the above formula.
A(n) = 5 + (n-1) 4
This is the function rule we needed. Note that there are infinitely many solutions to this exercise, we illustrated only one example.
Checking Our Answer
Substituting 6 Into the Function Rule
Let's check if the function rule describes a sequence that has 25 as the sixth term. To do so, we will substitute 6 for n into the function rule.
