(b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
A is true: As stated in the textbook (Note to the Reader, Ch. 5), if $a$, $b$, $c$ are in AP then $b = \frac{a+c}{2}$, i.e., $2b = a + c$. R is also true: The sum of first $n$ odd natural numbers = $n^2$ is a standard result. However, R has no connection to the condition for three terms to be in AP, so it does not explain A. Hence option (b).