Answer:
a(n) = 7n + 33
Explanation:
This sequence is arithmetic meaning it has a common difference. You can find this by subtracting a term from the term that comes after it. In this case, 47-40=7, so 7 is our common difference. Now we can start the formula where a(n)=7n+b, where a(n) is the value of a term and n is the number of the term. Now all we have to do is plug in some numbers.
a(n)=40 when n=1 as the first term of the sequence is 40. This means that 40=7(1)+b, or 40=7+b, or 33=b. This means that the explicit formula is a(n)=7n+33.