Analyzing the Number Series Pattern

The question asks us to find the missing number in the series: 8, 12, 16, 20, ?.

To find the missing number in a series, we need to identify the pattern or rule that connects the numbers.

Identifying the Pattern in the Series

Let's look at the difference between consecutive terms in the given number series:

• Difference between the second and first term: $$12 - 8 = 4$$
• Difference between the third and second term: $$16 - 12 = 4$$
• Difference between the fourth and third term: $$20 - 16 = 4$$

We can observe that the difference between each consecutive term is a constant value of 4. This indicates that the series is an arithmetic progression where each term is obtained by adding 4 to the previous term.

Finding the Missing Number

Following the identified pattern, the next term in the series (the missing number) will be obtained by adding 4 to the last given term, which is 20.

Missing number $$= \text{Last term} + \text{Common difference}$$

Missing number $$= 20 + 4 = 24$$

Therefore, the missing number in the series 8, 12, 16, 20, ? is 24.

Checking the Options

Let's compare our calculated missing number with the given options:

1. 24
2. 22
3. 32
4. 26

Our calculated missing number, 24, matches option 1.

Conclusion

The number series follows the pattern of adding 4 to the previous term. By applying this pattern, the missing number is found to be 24.

Revision Table: Number Series

Additional Information: Arithmetic Progressions

A number series where the difference between consecutive terms is constant is called an arithmetic progression (AP). This constant difference is known as the common difference ($$d$$).

The formula for the n-th term ($$a_n$$) of an arithmetic progression is:

$$a_n = a_1 + (n-1)d$$

where:

• $$a_n$$ is the n-th term
• $$a_1$$ is the first term
• $$n$$ is the term number
• $$d$$ is the common difference

In the given series: 8, 12, 16, 20, ?

• The first term ($$a_1$$) is 8.
• The common difference ($$d$$) is 4.
• We are looking for the 5th term ($$a_5$$).

Using the formula:

$$a_5 = a_1 + (5-1)d$$

$$a_5 = 8 + (4)4$$

$$a_5 = 8 + 16$$

$$a_5 = 24$$

This confirms our earlier result obtained by simply adding the common difference to the last term.