(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
The field is n times larger with n turns because current in each turn flows in the same direction, so magnetic fields due to each turn add up.
The source passage (12.2.3) directly states: "if there is a circular coil having n turns, the field produced is n times as large… because the current in each circular turn has the same direction, and the field due to each turn then just adds up." This makes (R) the precise reason for (A), so option (a) is correct.