Sequence Analysis: Finding the Missing Term

The question asks us to identify the missing number in the given sequence: 4, 9, 19, 39, ?

To find the missing term, we need to understand the pattern governing the sequence. Let's examine the relationship between consecutive terms:

Identifying the Pattern

• The first term is 4.
• The second term is 9.
• The third term is 19.
• The fourth term is 39.

Let's look at the difference between consecutive terms:

• Difference between the 2nd and 1st term: \(9 - 4 = 5\)
• Difference between the 3rd and 2nd term: \(19 - 9 = 10\)
• Difference between the 4th and 3rd term: \(39 - 19 = 20\)

The differences are 5, 10, 20. We can observe that each difference is double the previous difference (\(5 \times 2 = 10\), \(10 \times 2 = 20\)).

Alternatively, let's investigate another common pattern type: multiplying the previous term by a number and adding/subtracting a constant.

• From 4 to 9: We can try multiplying by 2 and adding 1. \((4 \times 2) + 1 = 8 + 1 = 9\). This works.
• From 9 to 19: Let's apply the same rule. \((9 \times 2) + 1 = 18 + 1 = 19\). This also works.
• From 19 to 39: Applying the rule again. \((19 \times 2) + 1 = 38 + 1 = 39\). This confirms the pattern.

The pattern is: Multiply the previous term by 2 and add 1 to get the next term.

Calculating the Missing Term

To find the missing term (the fifth term), we apply the identified pattern to the last known term (39):

Missing Term = \((39 \times 2) + 1\)

First, multiply 39 by 2:

\(39 \times 2 = 78\)

Next, add 1 to the result:

\(78 + 1 = 79\)

Therefore, the missing term in the sequence is 79.

Conclusion

The sequence follows the rule \(\text{Term}_{n} = (\text{Term}_{n-1} \times 2) + 1\). Based on this pattern, the missing term after 39 is 79.