Answer:
A(n) = 3 + 7(n-1)
Explanation:
Arithmetic sequences have common differences and change by the same amount between each term.
Arithmetic Sequences
Arithmetic sequences change by the same amount each term. In the sequence above, each term increases by 7. This means that 7 is added to the previous term to make the new term. Using this information we can write a function to represent this sequence.
Explicit Rule
The function that describes an arithmetic sequence is known as an explicit rule. Explicit rules are written as A(n) = A(1) + d(n-1). In this equation, A(1) represents the first term in a sequence and d represents the common difference. As you can see, the first term is 3, so A(1) = 3. The common difference is the change between terms. The previous paragraph shows that the common difference for this sequence is 7.
This means the explicit rule for this sequence is A(n) = 3 + 7(n-1).