Write a recursive formula for the arithmetic sequence.

Question

1 comma 13 comma 25 comma 37 comma ...
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Part 1
Choose the correct formula below.
A.
Upper A left parenthesis n right parenthesis equals Upper A left parenthesis n minus 1 right parenthesis minus 12​; ​A(1)equals1
B.
Upper A left parenthesis n right parenthesis equals Upper A left parenthesis n minus 1 right parenthesis plus 12​; ​A(1)equals1
C.
Upper A left parenthesis n right parenthesis equals Upper A left parenthesis n minus 1 right parenthesis plus 48​; ​A(1)equals1

Answer 1

To determine the correct recursive formula for the arithmetic sequence 1, 13, 25, 37, ..., we first need to identify the common difference.

1. The first term is 1.
2. The second term is 13, and the difference is \(13 - 1 = 12\).
3. The third term is 25, and the difference is \(25 - 13 = 12\).
4. The fourth term is 37, and the difference is \(37 - 25 = 12\).

The common difference between consecutive terms is 12.

Thus, the recursive formula for the sequence can be written as:

• \(A(n) = A(n - 1) + 12\); with the initial condition \(A(1) = 1\).

So the correct choice from the given options is:

B. \(A(n) = A(n - 1) + 12\); \(A(1) = 1\).