Number Pattern Fun
A sequence is just a list (a table is also a sequence). Example: the 3× table —
3
6
9
12
15
___
Jump: +3
🔎
Step 1 — Check the differences:
1a - Normal jumps
4
7
10
13
16
___
Look at how much each number increases or decreases.
Jumps:
+3
+3
+3
Answer : 19
Explanation: Every jump is +3. So 16 + 3 = 19.
2, 5, 8, 11, ___
10, 7, 4, 1, ___
101, 91, 81, 71, ___
"First check the jump — equal jumps mean simple steps!"
📈
Step 1b — Differences changing regularly
2
5
9
14
20
___
If the jumps are not equal, check if they change by a fixed rule.
Jumps:
+3
+4
+5
+6
Answer : 27
Explanation: Jumps increase by +1. Next jump = 6 + 1 = +7. So 20 + 7 = 27.
1, 3, 6, 10, ___
20, 15, 11, 8, ___
50, 55, 63, 74, ___
"If the jumps grow, a new pattern will show!"
📈
Step 1c — Cycle Patterns (Repeat Jumps)
1
3
6
7
9
12
___
Cycle jumps:
+2
+3
+1
+2
+3
Answer: 13
Explanation: Sometimes jumps repeat in cycles. Cycle jumps: +2, +3, +1 → repeat → next is +1 → Answer = 13
1, 3, 6, 10, 12, 15, ___
20, 15, 11, 8, 3, -1, ___
50, 55, 63, 74, 79, 87, ___
"If the steps repeat, the answer is sweet!"
✖️
Step 2 — Multiplication or division
1,
3,
9,
27,
___
Ratio:
×3,
×3,
×3
Answer : 81
Explanation: Multiply by 3 each time. 27 × 3 = 81.
5, 10, 20, 40, ___
81, 27, 9, 3, ___
2, 6, 18, 54, ___
"If it jumps too high, multiplication might apply!"
🧩
Step 3 — Mixed operations (repeat cycle)
2,
4,
12,
14,
42,
44,
___
Pattern:
+2,
×3,
+2,
×3,
+2
Answer : 132
Explanation: After 44 the next rule is ×3 → 44 × 3 = 132.
3, 6, 7, 14, 15, 30, ___
4, 8, 9, 18, 19, 38, ___
1, 4, 5, 20, 21, 84, ___
"Up, down, mix and match — look for a repeating batch!"
➕➕
Step 4 — Previous two add pattern
3,
4,
7,
11,
18,
___
Rule: Next = previous + one-before
Answer : 29
Explanation: 3+4=7, 4+7=11, 7+11=18 → 18 (previous) + 11 (one-before) = 29.
1, 2, 3, 5, 8, ___
2, 3, 5, 8, 13, ___
4, 6, 10, 16, 26, ___
"Add the last two to find the new!"
🟥
Step 5 — Square Number Sequences
1,
4,
9,
16,
___
Squares:
1²,
2²,
3²,
4²
→ next is 5²
Answer : 5² = 25
Explanation: The terms match square numbers: 1, 4, 9, 16 → these are 1², 2², 3², 4².
Continue the next square: 5² = 25.
4, 9, 16, 25, ___
36, 25, 16, 9, ___
1, 9, 25, 49, ___
"Square numbers climb like steps — 1², 2², 3²... nice and neat!"
🧊
Step 6: Cube Number Sequences
1,
8,
27,
64,
___
This is 1³, 2³, 3³, 4³ → next is 5³ = 125.
Answer: 125
Explanation: Each term is n³. So next is 5³ = 125.
8, 27, 64, 125, ___
125, 64, 27, ___
27, 64, 125, 216, ___
"Cubes climb fast, bigger than the last!"
📚
Squares & Cubes (1 → 12)
| n | n² (square) | n³ (cube) |
|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | 1331 |
| 12 | 144 | 1728 |
🔁
Step 7 — Frog Jumping patterns (Alternating patterns): split odd & even positions
1,
7,
3,
6,
5,
5,
___
Odd positions jumps:
1
+2=
3
+2=
5
Even positions jumps:
7
-1=
6
-1=
5
Answer : Next (position 7 → odd) = 7
Explanation: Odd terms 1 → 3 → 5 → next odd = 5 + 2 → 7.
1, 5, 2, 6, 3, 7, ___
2, 8, 3, 9, 4, 10, ___
1, 7, 3, 6, 5, 5, ___
"Odds do one, evens do another — they help each other!"
🔬
Step 8 — Sequence of a sequence
1,
2,
5,
14,
41,
___
Differences:
1
+1=
2
+3=
5
+9=
14
+27=
41
→ these jumps multiply by 3
Answer : Next difference = 27 × 3 = 81 → Next term = 41 + 81 = 122
Explanation: The first-level differences are 1, 3, 9, 27 (×3). Continue the jumping rule → 81; 41 + 81 = 122.
2, 6, 14, 30, ___
5, 12, 27, 58, ___
1, 4, 11, 26, ___
"When the jumps look wild, check the jumps’ child!"
🔤
Step 9 — VR Letter sequences
A,
C,
F,
J,
___
Convert letters to positions (A=1, B=2, C=3, D=4, E=5,...).
So A=1, C=3, F=6, J=10. The sequence is: 1, 3, 6, 10, ___.
Numbers:
+2,
+3,
+4 → Next: +5 → 10 + 5 = 15 → O
Answer : O
Explanation: The number pattern is +2, +3, +4, so next +5 → 10 + 5 = 15 → 15 = O.
B, E, H, K, ___
Z, X, V, T, ___
D, H, M, S, ___
"Turn letters into numbers — then spot the wonders!"
🎵
Final Poem to remember the tricks
Check the jumps, see if they match; if they grow, find the next step.
Split for two when things repeat; multiply when numbers leap.
Mix the moves, add the two, then check the jumps — and you'll get through!
