Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns - Free Printable

Let’s look at each row and find the pattern.

---

Row (i): Yellow circles

We see:
- First group: 1 circle
- Second group: 2 circles
- Third group: 3 circles
- Fourth group: 4 circles

So the next group should have 5 circles.

But wait — how are they arranged? The first is alone, then two side by side, then three in a triangle, then four in a square. So maybe the next one is five in a cross or pentagon? But since we’re just counting, the number is what matters.

✔ Pattern: +1 each time → Next = 5 circles

---

Row (ii): Stars (green and red)

Sequence:
Green, Green, Red, Green, Green, Red, Green, Green, ?

Look at the positions of red stars:
- Position 3: Red
- Position 6: Red
→ So every 3rd star is red.

That means position 9 should be Red.

Also, the green stars fill the rest.

So after “Green, Green”, the next is Red.

✔ Pattern: Every 3rd star is red → Next = Red star

---

Row (iii): Blue circles

Groups:
- First: 1 circle
- Second: 3 circles (triangle)
- Third: 5 circles (like a bigger triangle or pyramid)

Wait — let’s count:

Group 1: 1
Group 2: 3
Group 3: 5

That’s increasing by 2 each time: 1, 3, 5 → next should be 7

Check arrangement:
- 1 = single
- 3 = triangle (1 on top, 2 below)
- 5 = maybe 1 on top, 2 middle, 2 bottom? Or 3 on bottom, 2 above? Actually, looking at image: third group has 5 — looks like 3 on bottom, 2 stacked on top? Wait no — actually it's 1 on top, 2 in middle, 2 on bottom? Hmm.

Actually, standard triangular numbers:
Triangular numbers: 1, 3, 6, 10... but here it’s 1, 3, 5 — that’s odd numbers.

So likely: 1, 3, 5, 7 → next is 7 circles

✔ Pattern: Odd numbers → Next = 7 circles

---

Row (iv): Triangles and stars

Sequence:
Green triangle, Yellow star, Green triangle, Green triangle, Yellow star, Yellow star, Green triangle, Green triangle, Green triangle, ?

Let’s list them with positions:

1. △ (green)
2. ★ (yellow)
3. △
4. △
5. ★
6. ★
7. △
8. △
9. △
10. ?

Now group them:

First block: △, ★ → 1 triangle, 1 star
Second block: △, △, ★, ★ → 2 triangles, 2 stars
Third block: △, △, △, ? → so far 3 triangles, need 3 stars?

Wait — let’s see the pattern of blocks:

Block 1: 1 triangle, 1 star → total 2 items
Block 2: 2 triangles, 2 stars → total 4 items
Block 3: should be 3 triangles, 3 stars → total 6 items

In the sequence:

Positions 1–2: Block 1
Positions 3–6: Block 2 (△,△,★,★)
Positions 7–12: Block 3 → starts with 3 triangles (positions 7,8,9), then should be 3 stars (positions 10,11,12)

So position 10 should be Yellow star

✔ Pattern: Blocks increase by 1 triangle and 1 star each time → Next = Yellow star

---

Row (v): Orange concentric circles

First: small solid circle (1 ring?)
Second: medium with 2 rings (outer + inner)
Third: large with 3 rings

Count the rings:

- First: 1 ring (just the circle itself)
- Second: 2 rings (inner circle + outer ring)
- Third: 3 rings (center + middle + outer)

So next should have 4 rings

✔ Pattern: Number of rings increases by 1 → Next = 4-ring circle

---

Now, let’s write the answers for each blank:

(i) 5 yellow circles
(ii) 1 red star
(iii) 7 blue circles
(iv) 1 yellow star
(v) 1 orange circle with 4 rings

But since the blanks are lines, probably we just write the number or describe simply.

Looking back at the problem — it’s likely expecting the *number* of objects or the *next item*.

For (i), (iii), (v) — it’s about quantity.

For (ii), (iv) — it’s about type/color.

But in all cases, the blank is after the sequence, so we put the next thing.

Since it’s a worksheet, probably they want:

(i) 5
(ii) red star
(iii) 7
(iv) yellow star
(v) 4 rings (or just 4)

But to match format, perhaps write the count or description.

Wait — in row (i), the groups are shown as clusters, and blank is for next cluster — so answer is "5 circles"

Similarly, (iii) "7 circles"

(v) "circle with 4 rings"

But for simplicity, since it’s math-only-math.com, likely numerical answers where possible.

Looking again:

In (i), the groups are 1,2,3,4 → next 5

In (ii), pattern every 3rd is red → 9th is red

In (iii), 1,3,5 → next 7

In (iv), block pattern → next is star

In (v), rings: 1,2,3 → next 4

So final answers per row:

(i) 5
(ii) red star
(iii) 7
(iv) yellow star
(v) 4

But to be precise, let’s confirm (v):

First figure: solid dot — can be considered 1 layer
Second: two concentric circles — 2 layers
Third: three concentric circles — 3 layers
So fourth: 4 layers → 4 rings

Yes.

Now, for the answer format — since the user didn’t specify, but it’s a fill-in-the-blank, I’ll write the expected content for each blank.

Final Answer:

(i) 5
(ii) red star
(iii) 7
(iv) yellow star
(v) 4