How to find the next number in a simple arithmetic sequence like 5, 11, 17, 23.

Numbers have a way of telling stories, even when they’re tucked inside a test. On the HSPT math section, many of the quiet stories come as sequences. They’re not scary once you hear their rhythm. Here’s one that pops up often: 5, 11, 17, 23, … What comes next?

Let me explain the neat trick behind these patterns.

The pattern in this sequence is a steady, predictable bump. Each step moves up by the same amount. In math terms, that means we’re looking at an arithmetic sequence. The word “arithmetic” might sound fancy, but it’s really just a fancy way of saying the jumps between numbers are constant.

A simple walk-through, step by step

• Start with what you know: 5, 11, 17, 23. Look at how much we add each time.

• Subtract successive terms to find the gap: 11 minus 5 gives 6; 17 minus 11 gives 6; 23 minus 17 gives 6. The difference is consistently 6.

• Since the jump is always 6, the next number is simply the current last number plus 6: 23 + 6 = 29.

• So, the next term is 29. In the multiple-choice setup, that’s option C.

This is a tiny, perfect example of pattern recognition that appears again and again in the HSPT’s math questions. It’s not about memorizing a lot of tricks; it’s about seeing the rhythm and following it.

A little perspective helps, too

Think of it like stairs. Each stair step is six inches higher than the one before. If you start on the first step at height five, you climb to 11, then 17, then 23, and the next step brings you to 29. The rule is simple: add six each time. When you see a string of numbers that keeps stepping up by the same amount, you’re probably looking at an arithmetic sequence.

That sense of order isn’t just for tests. It’s all around us—schedules, budgets, even game scores. When you recognize the pattern, you decode the story behind the numbers faster. And yes, that little realization can shave minutes off a problem, which is a nice win in any math section.

Why this kind of sequence matters in real life

• Scheduling: If a bus leaves every 6 minutes starting at a certain time, the arrival times line up in a tidy pattern, making it easy to predict when the next bus will come.

• Budgeting: When you add the same amount to a balance each week, you can forecast your total after several weeks, without pulling out a calculator every time.

• Sports analytics: If a player keeps scoring in fixed increments, you can project future performances with simple arithmetic rather than complex models.

A quick, friendly drill you can try

Here’s a tiny set you can test yourself on, just to feel the rhythm:

• Start with 2, 7, 12, 17. What’s the next number?

• Try a two-step version: 10, 16, 22, 28. What comes next?

If you watch the differences, you’ll notice they’re both adding 5 in the first set and adding 6 in the second. It’s a small reminder that the core idea is constant difference, not a complicated trick.

Tips to tune this kind of thinking for the HSPT math section

• Look for the difference, not the digits. The actual jump matters more than the digits themselves.

• Check a couple of gaps. If the gaps are all the same, you’ve found an arithmetic sequence.

• Don’t fear the simplest answer. When the pattern is clear, the next term is usually a straightforward addition.

• Use a quick check. After you find the next term, add it to the last known term and see if the result still follows the same jump.

A touch of strategy if you’re staring at a similar problem

• Identify the pattern first: is the difference constant? Is there a consistent ratio? Sometimes you’ll see a sequence that doubles or follows a different rule, but many HSPT questions cling to a steady increase.

• Write it down briefly. A tiny scratch work line like “5, 11 (+6), 17 (+6), 23 (+6)” helps you keep the flow intact in your head and on paper.

• Verify with a quick back-check. If you add 6 to 29, you’d get 35, which would fit the same pattern for the next term. If the numbers started to break the pattern, you’d reassess.

Where this pattern sits in the bigger picture

Arithmetic sequences are one of those building blocks that show up across math, not just on tests. They sync nicely with algebra concepts, like variables and linear equations, because they boil down to adding a fixed amount. When you’re comfortable with this, you’re better equipped to tackle more complex sequences, where the jump might change or depend on position. The core skill is the same: notice the rule, follow it, and check your logic.

A few more bites of context, quickly

• If you ever see a sequence like 3, 9, 15, 21, you’ll spot the difference is 6 again. The next term would be 27. It’s not that every problem borrows the same numbers; it’s that the method—the constant difference—travels reliably.

• For sequences that grow by multiplying rather than adding, you’ll switch into a different pattern—ratios rather than differences. That’s a separate, just-as-important tool in your math toolkit.

A gentle nudge toward mastery

The next time you’re faced with a sequence on the HSPT, pause for a moment and listen for the rhythm. If the jumps feel uniform, you’re likely in arithmetic country. The answer is often a clean, small step away from the last term. It’s less about memorizing a pile of tricks and more about training your eye to notice the most reliable clue: the difference.

If you want a little more challenge without leaving the lane, try this thought exercise: create your own short sequence with a fixed difference, then flip the process—start with the last number you chose and work backward by the same step. It’s a fun way to confirm you understand the rule and to feel how flexible these patterns can be when you switch perspectives.

A closing thought, with a smile

Numbers aren’t just tools; they’re stories we can read with a clear set of steps and a calm mind. When you approach a sequence like 5, 11, 17, 23, …, you’re not facing a wall of algebra. You’re listening for a beat—the six-step cadence that keeps the story moving upward. The next line in the tale, in this case, is 29. It’s a small note, but it lands with confidence, a sign that you’re getting the hang of it.

If this kind of pattern feels approachable, you’re likely to enjoy the other math stories you’ll encounter. Think of each problem as a tiny puzzle with a friendly rule hiding in plain sight. When you tap into that rhythm, you’ll find your flow, and with it, a steadier stride through the section.