Look at the pattern of shaded numbers. use place value to describe how the number change.

501 is shaded,502,503,504,505,506,507,508,509,510,511,512,513 is shaded,514,515,516,517,518,519,520,521,522,523,524,525 is shaded,526,527,528,529,530,531,532,533,534,535,536,537 is shaded,538,539,540,541,542,543,544,545, 546,547,548,549 is shaded,550

To look at the pattern of shaded numbers, we need to observe how the numbers change based on their place value.

From the given sequence, we can see that the shaded numbers start with 501 and then increase by 1 repeatedly until they reach 549. Let's break this down:

Initially, the hundreds place remains constant at 5.
The tens place starts at 0 and increases by 1 until it reaches 9, at which point it resets back to 0 and the hundreds place increases by 1.
The ones place starts at 1 and increments by 1 until it reaches 9, at which point the tens place increases by 1, and the ones place resets back to 0.

So, using place value, we can conclude that the shaded numbers change by 1 in the ones place until it reaches 9, at which point the tens place increases by 1 and the ones place resets to 0.

To verify this pattern, we can continue the sequence:
551, 552, 553, 554, 555, 556, 557, 558, 559, 560, ...

Thus, the next shaded number after 550 would be 551.