Sequences / Skips up to 100: Jumps of 100

The sequence provided is $200, 300, 400, \ldots$. To determine the pattern, calculate the difference between consecutive terms:

• The difference between $300$ and $200$ is $100$.
• The difference between $400$ and $300$ is $100$ again.

This confirms the sequence increases by $100$ for each successive term. To extend this sequence:

• Add $100$ to $400$ to get $500$.
• Add $100$ to $500$ to get $600$.
• Add $100$ to $600$ to get $700$.

Thus, the sequence continued is: $200, 300, 400, 500, 600, 700$.

The correct answer is:
$200,300,400,500,600,700$

The sequence problem requires us to determine what numbers fill the gaps between 300, 500, and 600, while continuing this sequence. We first check the difference between these numbers. From 300 to 500, the difference is $500 - 300 = 200$. However, the same difference applies in a smaller segment like 300 and the next logical missing number:

• Check the logical step between 500 and 300. The number in between them is logical at $500 - 100 = 400$, by assuming a consistent stepwise increase.
• Similarly, between 500 to 600, the difference also suggests stepping up 600 from another calculated basis of 100 to establish the pattern: $500 + 100 = 600$.

Continuing this observation from 300 forward:

Starting from 300:

1. Add 100 to 300 to get 400.
2. Add 100 to 400 to arrive at 500.
3. Similarly, add 100 to get 600, and continuing this pattern:

• From 600, add another 100 yields 700.
• We can see the sequence continues with this regular step, leading ultimately to $800$.

The consistent pattern ensures the sequence emerges as $300, 400, 500, 600, 700, 800$.

This sequence matches one of the given options:

To conclude, the completed sequence is $300, 400, 500, 600, 700, 800$.