Assertion (A): $a$, $b$, $c$ are in A.P. if and only if $2b = a + c$.

Reason (R): The sum of first $n$ odd natural numbers is $n^2$.

Question

Assertion (A): $a$, $b$, $c$ are in A.P. if and only if $2b = a + c$.

Reason (R): The sum of first $n$ odd natural numbers is $n^2$.

Accepted Answer

Step 1: Assertion: If $a, b, c$ are in A.P., then $b - a = c - b \Rightarrow 2b = a + c$. True. Reason: Sum of first $n$ odd numbers $= 1 + 3 + 5 + \ldots + (2n-1) = n^2$. True. But R does not explain A.

Question

Solution