NCERT Solutions Class 5 Maths Chapter 7 Can You See the Pattern ... - Free Printable

Let's solve the problem step by step and understand the pattern.

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Problem Statement:

Take any number (here, 12). Multiply it by 2, 3, 4, ..., and add 3 to each result. Check if the difference between consecutive answers is constant.

We are given:

```
12 × 2 + 3 = 27
12 × 3 + 3 = 39
12 × 4 + 3 = 51
12 × 5 + 3 = 63
...
```

We need to continue this pattern and fill in the blanks.

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Step-by-step Calculation:

Let’s compute each missing value.

#### 1. $ 12 \times 6 + 3 $
$$
12 \times 6 = 72 \\
72 + 3 = 75
$$

✔ So, first blank = 75

#### 2. $ 12 \times 7 + 3 $
$$
12 \times 7 = 84 \\
84 + 3 = 87
$$

✔ Second blank = 87

#### 3. $ 12 \times 8 + 3 $
$$
12 \times 8 = 96 \\
96 + 3 = 99
$$

✔ Third blank = 99

#### 4. $ 12 \times 9 + 3 $
$$
12 \times 9 = 108 \\
108 + 3 = 111
$$

✔ Fourth blank = 111

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Now, let's write the full table:

| Step | Expression | Result |
|------|-------------------|--------|
| 1 | 12 × 2 + 3 | 27 |
| 2 | 12 × 3 + 3 | 39 |
| 3 | 12 × 4 + 3 | 51 |
| 4 | 12 × 5 + 3 | 63 |
| 5 | 12 × 6 + 3 | 75 |
| 6 | 12 × 7 + 3 | 87 |
| 7 | 12 × 8 + 3 | 99 |
| 8 | 12 × 9 + 3 | 111 |

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Check the Differences Between Consecutive Results:

- 39 - 27 = 12
- 51 - 39 = 12
- 63 - 51 = 12
- 75 - 63 = 12
- 87 - 75 = 12
- 99 - 87 = 12
- 111 - 99 = 12

✔ The difference is always 12 at every step.

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Why is the difference constant?

Let’s generalize:

Let the number be $ x $.
At each step, we compute:
$$
x \times n + 3
$$
where $ n $ increases by 1 each time.

So,
- Step $ n $: $ x \times n + 3 $
- Step $ n+1 $: $ x \times (n+1) + 3 $

Difference:
$$
[x(n+1) + 3] - [xn + 3] = xn + x + 3 - xn - 3 = x
$$

So, the difference between consecutive results is equal to the original number (x).

Here, $ x = 12 $, so the difference is always 12.

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✔ Final Answer:

The missing values are:

- $ 12 \times 6 + 3 = 75 $
- $ 12 \times 7 + 3 = 87 $
- $ 12 \times 8 + 3 = 99 $
- $ 12 \times 9 + 3 = 111 $

And yes, the difference between each result is always 12, which is the same as the original number.

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🔍 Conclusion:

Yes, the difference in the answer is the same at every step — it is equal to the original number (12). This is a consistent pattern.