Multiple choice (select 1 out of 4 options for the question below)Identify the missing number in the series 33, ?, 19, 12, 5  Question 5Answera.29b.26c.31d.27

1. Break Down the Problem

We need to identify the missing number in the series: 33, ?, 19, 12, 5. Observing the patterns in the differences between consecutive numbers might help us uncover the missing number.

2. Relevant Concepts

To find the missing number, we can subtract consecutive terms to see if there is a consistent pattern in the differences:

• Difference between the second value and the first value (33 and ?)
• Difference between the unknown value and the third value (19)
• Difference between other consecutive numbers (19 to 12, and 12 to 5)

3. Analysis and Detail

Let's calculate the differences from 19 to 12 and 12 to 5:

• $19 - 12 = 7$
• $12 - 5 = 7$

This shows that the difference is consistently 7 between these two pairs.

Now, we can apply this to the missing number:

• Let the unknown number be $x$. Therefore, we assume $19 - x = 7$.

• Solving for $x$:

  $x = 19 - 7 = 12$

To maintain the sequence, we look back to the value before 19:

• $33 - x = 7$ (Using the first difference similar to others)

We can also set up:

• $33 - x = 14$ (previous difference since $19 - 12 = 7$ )

• Solving for $x$:

  $x = 33 - 14 = 19$

To summarize the previous numbers:

• 33 to x: 14
• x=26
• 26 to 19: 7
• 19 to 12: 7
• 12 to 5: 7

4. Verify and Summarize

The verified missing number in the series is 26, which fits the established differences. Therefore, the series completes as 33, 26, 19, 12, 5.

Final Answer

The missing number is 26 (Option b).