What will be the maximum sum of $44, 42, 40, \dots$ ?

The given sequence is an Arithmetic Progression (AP) where:

• First term, $a = 44$

• Common difference, $d = 42 - 44 = -2$

To maximize the sum, we must include all positive terms (and optionally zero, which does not alter the sum).

Find the number of positive terms $n$:

• The $22^{\text{nd}}$ term is $a_{22} = 44 + (22 - 1)(-2) = 2$.

• The $23^{\text{rd}}$ term is $a_{23} = 44 + (23 - 1)(-2) = 0$.

Sum of the first $n = 22$ (or $n = 23$) terms:

Thus, the maximum sum is 506 (Option C).