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🤖 Logic Robot's Number Sequence Quest

Master number sequences by spotting hidden rules, cracking patterns, and predicting the next term like a true Logic Lab detective.

🤖 Beep boop! Welcome to the Logic Lab, brilliant thinker! I'm Logic Robot, and today we're cracking one of the most powerful puzzles in Verbal Reasoning: **number sequences**. Here's a surprising fact — the whole universe runs on patterns! The petals on a sunflower, the way a snail's shell curls, even the beats in your favourite song follow hidden number rules. Long ago, a clever mathematician noticed that rabbits multiplied in a repeating pattern, and that discovery is still used by computer programmers, video game designers and even the people who plan the fastest routes for delivery lorries. When you learn to spot patterns, you're training your brain to think like an inventor, a coder, or a detective. In your 11+ exam, examiners love number sequences because they show how quickly and neatly your brain can find order in a jumble of numbers. But here's the best part — once you know my secret methods, these puzzles feel less like tricky tests and more like exciting games. So put on your thinking goggles, because by the end of this lesson, you'll be able to look at a line of numbers and reveal the hidden rule hiding inside. Ready? Let's power up! ⭐

So, what exactly is a **number sequence**? A number sequence is simply a list of numbers that follow a special rule, one after another. Each number in the list is called a **term**. Think of it like a line of stepping stones across a river — each stone is placed a certain distance from the last one, and if you know that distance, you can guess exactly where the next stone will be. For example, in the sequence 2, 4, 6, 8, the rule is 'add 2 each time', so the next stepping stone would be 10. The rule is the magic key that unlocks the whole puzzle. Some rules are gentle and steady, like adding the same number over and over. Others are sneakier — they might multiply, or the gaps between the numbers might grow bigger and bigger. Some sequences even weave two patterns together, like two dancers taking turns. Your job as a Logic Lab detective is always the same: find the rule, then use it to predict the next term. Once you can name the rule in words — 'add 3', 'double it', 'the gaps grow by one' — you've basically solved the puzzle. Simple, isn't it?

Let's explore **how sequences work** under the bonnet. The most common type is a **linear sequence**, where you add or subtract the same number every time. That number is called the **common difference**. In 5, 8, 11, 14, the common difference is +3. To find it, subtract any term from the one after it: 8 − 5 = 3. Easy! But watch out — sometimes numbers get *smaller*, like 20, 17, 14, 11. Here the common difference is −3, meaning you subtract 3 each step. Then there are **multiplying sequences**, like 3, 6, 12, 24, where each term doubles (×2). Trickier still are sequences where the **gap itself changes**. Look at 1, 3, 6, 10, 15. The gaps are +2, +3, +4, +5 — growing by one each time! These are sometimes called **triangular numbers**. Finally, some sequences are **interleaved**, meaning two patterns take turns. In 1, 10, 2, 20, 3, 30, one pattern (1, 2, 3) hides among another (10, 20, 30). The secret to every type is the same: write down the gaps between the terms. Those gaps whisper the rule to you. Once you hear it, the sequence has no more secrets. 🧠

Here is my trusted step-by-step **method** for cracking any number sequence. Follow these steps in order every single time: **Step 1 — Write the gaps.** Look at the difference between each pair of neighbouring terms and jot it down underneath. **Step 2 — Check if the gaps are the same.** If they are, you've found a linear sequence — just add (or subtract) that common difference to get the next term. **Step 3 — If the gaps are NOT the same, look at the gaps of the gaps.** Are they growing steadily, like +1, +2, +3? That tells you the pattern is speeding up. **Step 4 — Test for multiplying.** Ask: 'Is each term double, triple, or half the one before?' Try dividing a term by the one before it. **Step 5 — Check for interleaving.** If the numbers jump wildly up and down, look at every OTHER number — there may be two hidden patterns taking turns. **Step 6 — Predict and check.** Use your rule to work out the next term, then test your rule on the WHOLE sequence to make sure it works everywhere, not just once. This last step is your safety net — it catches careless mistakes. Follow these six steps calmly, and no sequence can outsmart you!

Let's warm up with a **simple worked example**: 4, 7, 10, 13, ___. First, I follow my method. **Step 1 — write the gaps.** From 4 to 7 is +3. From 7 to 10 is +3. From 10 to 13 is +3. **Step 2 — are the gaps the same?** Yes! Every gap is +3, so this is a lovely linear sequence with a common difference of +3. **Step 6 — predict.** To find the next term, I add 3 to the last number: 13 + 3 = 16. So the answer is **16**. Now let me double-check by testing the rule across the whole sequence: 4 (+3) 7 (+3) 10 (+3) 13 (+3) 16. Perfect — it works every time! Notice how I didn't rush or guess. I calmly wrote the gaps first, because that one small habit makes the rule pop out instantly. A common wobble here is to accidentally add 3 to the wrong number, like adding to 10 instead of 13. Always add to the LAST term shown. If you can spot the +3 pattern and land on 16, you've mastered the most important type of sequence in the whole exam. Well done, detective! ⭐

Now for a **medium example** with a little twist: 2, 3, 5, 8, 12, ___. Let's use my method. **Step 1 — write the gaps.** From 2 to 3 is +1. From 3 to 5 is +2. From 5 to 8 is +3. From 8 to 12 is +4. **Step 2 — are the gaps the same?** No — they are 1, 2, 3, 4. **Step 3 — look at the gaps of the gaps.** They grow by exactly +1 each time. This is where lots of pupils slow down, because they expect a single steady number and panic when the gaps change. Don't worry — a *changing* gap is still a clear pattern! Since the gaps go 1, 2, 3, 4, the next gap must be +5. **Step 6 — predict.** Add that to the last term: 12 + 5 = 17. So the answer is **17**. Let me check the whole thing: 2 (+1) 3 (+2) 5 (+3) 8 (+4) 12 (+5) 17. It works beautifully! The trap here is assuming the gap stays at +4, which would give 16 — a very tempting wrong answer. Whenever the gaps aren't equal, always ask, 'How are the gaps themselves changing?' That single question turns a scary sequence into an easy one.

Here's how this appears in a real **GL or CEM exam**. Question: *What number continues this sequence?* 6, 11, 21, 41, 81, ___. Options: **A) 121 B) 141 C) 161 D) 162**. Let's crack it with my method. **Step 1 — write the gaps.** 11 − 6 = 5. 21 − 11 = 10. 41 − 21 = 20. 81 − 41 = 40. The gaps are 5, 10, 20, 40 — they DOUBLE each time! **Step 4 — this is a multiplying-gap pattern.** The next gap must be 40 × 2 = 80. **Step 6 — predict.** 81 + 80 = 161. So the answer is **C) 161**. ✅ Now, why are the wrong options so tempting? **A) 121** comes from wrongly adding 40 again (81 + 40), assuming the gap stayed the same. **B) 141** comes from a careless doubling of 81 minus a bit — a panic guess. **D) 162** comes from simply doubling 81 (81 × 2), because pupils spot 'doubling' but apply it to the wrong thing — you double the GAP, not the term. This is the examiner's classic trap: they reward you for finding the *precise* rule, not just any rule. Always test your rule across the whole sequence before you commit. Calm, careful, correct — that's how top-grammar pupils earn their marks. 🏆

Let's finish with the **three most common mistakes** and how to beat them. **Mistake 1: Only checking the first gap.** A pupil sees 4, 7 and shouts '+3!' without checking the rest. Fix: ALWAYS write every gap — the pattern lives in all of them, not just the first. **Mistake 2: Confusing 'doubling the term' with 'doubling the gap'.** When gaps double (5, 10, 20…), pupils sometimes double the whole number instead. Fix: remember my chant — 'The gap is the thing that grows, not the number below.' **Mistake 3: Missing interleaved sequences.** When numbers jump up and down wildly (1, 10, 2, 20, 3…), pupils try to find one rule and get stuck. Fix: circle every OTHER number and hunt for two separate patterns taking turns. My #1 power tip for exam day: **write the gaps underneath the numbers in tiny pencil marks.** This one habit turns invisible patterns into visible ones and saves you from silly slips. Then always do the final check — test your rule on the whole line. Do these things, and number sequences become your easiest, fastest marks in the entire paper. You've got this, super-detective! Beep boop — Logic Robot is proud of you! 🎯

Common mistakes

Frequently asked questions

Why do we even need to learn number sequences?

Because they train your brain to spot patterns quickly — a skill used by coders, scientists and puzzle-solvers everywhere! In the 11+ they're some of the fastest marks to earn. Keep practising and they'll feel easy. ⭐

What if I can't see the rule straight away?

Don't panic! Just write the gaps between the numbers in tiny pencil marks. The pattern almost always jumps out once you see the gaps. Slow and steady beats a rushed guess. You've got this! 🤖

How do I know if it's adding or multiplying?

Try both! First check if the gaps are the same (adding). If the numbers grow really fast, try dividing one term by the one before — if you get the same answer, it's multiplying. Testing is smart, not slow. 🧠

What are those weird sequences that jump up and down?

Those are interleaved sequences — two patterns hiding together and taking turns. Circle every other number to reveal each hidden pattern. Once you spot both, they're actually quite fun! Keep hunting. 🔍

What if I forget the six-step method in the exam?

Just remember the golden first move: write the gaps. That one habit unlocks nearly every sequence. Everything else follows from there. Trust your practice — your brain remembers more than you think! 🎯

How can I check my answer is definitely right?

Test your rule across the WHOLE sequence, not just the last step. If it works for every gap from start to finish, you can be confident. This final check catches silly slips. Brilliant thinking! 🏆