Class-5, Mathematics, Can You See the Patterns? worksheet | Live ... - Free Printable

Let's solve the worksheet step by step.

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Question 1: What is the growth interval for the following sequences?

We are to find the pattern (either increasing or decreasing) in each sequence and determine the growth interval — i.e., how much each number increases or decreases by.

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(a) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
- Check the difference between consecutive numbers:
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
...and so on.
✔ These numbers grow by 2.

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(b) 45, 40, 35, 30, 25, 20, 15, 10, 5
- Check the difference:
40 - 45 = -5
35 - 40 = -5
30 - 35 = -5
...so it's decreasing by 5.
✔ These numbers reduce by 5.

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(c) 5, 10, 15, 20, 25, 30, 35, 40, 45
- Differences:
10 - 5 = 5
15 - 10 = 5
20 - 15 = 5
...continuing.
✔ These numbers grow by 5.

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(d) 27, 24, 21, 18, 15, 12, 9, 6, 3
- Differences:
24 - 27 = -3
21 - 24 = -3
18 - 21 = -3
...so decreasing by 3.
✔ These numbers reduce by 3.

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✔ Answers for Question 1:

(a) Grow by 2
(b) Reduce by 5
(c) Grow by 5
(d) Reduce by 3

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Question 2: Complete the following pattern

We need to identify the pattern and choose the correct figure to complete it.

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#### a) Smileys Pattern

Sequence:
1. 😊 (happy face)
2. 😐 (neutral face, eyes closed)
3. 😌 (sad face, frowning)

Now we look at the changes:

- First → Second: Mouth goes from smile to straight line (neutral), eyes stay same.
- Second → Third: Mouth goes from neutral to frown (sad).
- So the pattern is: Happy → Neutral → Sad

Now, what comes next?

After sad, logically, it might go back to neutral or happy? But let’s check the options.

Options:
- (i) 😐 (neutral with dots)
- (ii) 🙂 (happy with dots)

But notice: the third face has a frown, and the second had a straight mouth.

So the pattern of mouths:
- 😊 → 😐 → 😌 → ?

This looks like a cycle:
Smile → Straight → Frown → ?
Maybe back to Straight or Smile?

Wait — but the second face is already neutral (straight). The third is frown.

So if it's going:
Smile → Neutral → Sad → ???

Then perhaps it cycles back to Neutral?

But let's look more closely at the shapes:

Actually, the eyes are also changing slightly.

- First: two dots (eyes open)
- Second: two dots (same)
- Third: two dots (same)

No change in eyes.

Mouths:
- First: U-shaped (smile)
- Second: straight line
- Third: upside-down U (frown)

So the pattern is: U → straight → upside-down U

Next should be straight again? Or maybe cycle back?

But that would make it: U → straight → upside-down U → straight → U...

But we’re only going forward.

But wait — the sequence is:

1. 😊 (U)
2. 😐 (straight)
3. 😌 (upside-down U)

So the pattern is: U → straight → upside-down U

Now, what comes after upside-down U?

It could go back to straight, then U, etc.

But we have only two options:

(i) 😐 (straight mouth, dots) → matches second one
(ii) 🙂 (U-shaped mouth, dots) → matches first one

Since the third is frown (upside-down U), the next logical step is to return to neutral (straight), as it's a cycle.

So the sequence is:
Smile → Neutral → Sad → Neutral → Smile...

Hence, next should be Neutral → which is option (i)

✔ So answer for (a): (i)

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#### b) Arrow Pattern

Sequence:
1. ←→ (left-right arrow)
2. ↑↓ (up-down arrow)
3. ↔ (double-headed horizontal arrow, but pointing left and right with T-like shape?)

Wait — let's analyze carefully.

Look at the arrows:

1. Left and right arrows connected: ←→
2. Up and down arrows connected: ↑↓
3. Then: ↔ — but this is a single double-headed arrow pointing both ways horizontally.

Wait — actually, the third one looks like:
A horizontal arrow with a T-shape — it's like a double-headed arrow but with a crossbar?

Wait — looking closely:

- First: ←→ (two arrows opposite directions, same line)
- Second: ↑↓ (up and down arrows)
- Third: ↔ — but drawn as a single horizontal double-headed arrow

Wait — actually, the third one is not just ↔ — it's a horizontal arrow with arrowheads on both ends, like a bidirectional arrow.

But the first is also a bidirectional arrow (←→).

So why is the third different?

Wait — look at the shape:

- First: ←→ (simple left-right arrows)
- Second: ↑↓ (up-down arrows)
- Third: ↔ — but with a small bar in the middle? Actually, no — it's just a bidirectional horizontal arrow.

Wait — maybe it's about rotation?

Let’s think differently.

Look at the direction:

1. ←→ → horizontal
2. ↑↓ → vertical
3. ↔ → horizontal again

So pattern: horizontal → vertical → horizontal → ?

Then next should be vertical?

But the options are:

(i) ↓↑ (down-up, vertical)
(ii) ←→ (left-right, horizontal)

Wait — but the third is ↔, which is horizontal.

So sequence:
Horizontal → Vertical → Horizontal → Vertical

So next should be vertical, which is (i)

But (i) is ↓↑ — same as ↑↓ but reversed.

But direction doesn't matter — it's still vertical.

So likely, the pattern is alternating: horizontal, vertical, horizontal, vertical

So next should be vertical → (i)

✔ Answer: (i)

Alternatively, could it be based on rotation?

But since the third is horizontal, and first was horizontal, second vertical, so it alternates.

Yes.

So the pattern is:
- 1st: horizontal
- 2nd: vertical
- 3rd: horizontal
- 4th: vertical → (i)

✔ So answer for (b): (i)

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✔ Final Answers:

#### Question 1:
(a) Grow by 2
(b) Reduce by 5
(c) Grow by 5
(d) Reduce by 3

#### Question 2:
(a) (i)
(b) (i)

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📝 Explanation Summary:

- In Question 1, we identified the common difference between consecutive terms.
- In Question 2, we looked for repeating patterns in facial expressions and arrow directions.
- For smileys: Smile → Neutral → Sad → Neutral → so (i)
- For arrows: Horizontal → Vertical → Horizontal → Vertical → so (i)

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✔ Final Answers:

1.
(a) 2
(b) 5
(c) 5
(d) 3

2.
(a) (i)
(b) (i)