GATE CS 2013 Q58 — General Aptitude

The given sequence is an Arithmetic Progression (AP):

$$44, 42, 40, \dots$$

Here, the first term is $a = 44$ and the common difference is $d = 42 - 44 = -2$.

To obtain the maximum sum, we must sum all the positive terms of the sequence. Adding any negative term would decrease the total sum. (Adding $0$ does not change the sum).

Let the $n$-th term be the last positive term ($a_n > 0$):

$$a + (n-1)d > 0$$

$$44 + (n-1)(-2) > 0$$

$$44 - 2n + 2 > 0$$

$$46 > 2n \implies n < 23$$

Since $n$ must be an integer, the number of positive terms is $n = 22$.

The $22^{\text{nd}}$ term is:

$$a_{22} = 44 + (22-1)(-2) = 2$$

The sum of these $22$ terms is given by the formula:

$$S_n = \frac{n}{2} (a + a_n)$$

$$S_{22} = \frac{22}{2} (44 + 2)$$

$$S_{22} = 11 \times 46 = 506$$

Therefore, the maximum sum of the sequence is 506.