Finding the Incorrect Number in the Series

Let's examine the given series of numbers: 8, 14, 26, 48, 98, 194. We need to identify the number that does not fit the pattern followed by the rest of the series. This type of problem requires finding the underlying logical rule connecting the consecutive numbers.

Analyzing the Number Series Pattern

Let's try to find a relationship between each number and the next one in the sequence.

• From 8 to 14: \(8 \times 2 = 16\), and \(16 - 2 = 14\).
• From 14 to 26: \(14 \times 2 = 28\), and \(28 - 2 = 26\).
• From 26 to 48: \(26 \times 2 = 52\), and \(52 - 2 = 50\). The number in the series is 48. This looks like a potential break in the pattern.

Let's assume the pattern is multiplying the previous number by 2 and then subtracting 2. The general form of the pattern seems to be: \(n_{i+1} = n_i \times 2 - 2\).

Applying the Pattern Step-by-Step

Let's apply this rule starting from the first term to see which number deviates.

1. First term: 8
2. Expected second term: \(8 \times 2 - 2 = 16 - 2 = 14\). Actual second term is 14. This matches.
3. Expected third term: \(14 \times 2 - 2 = 28 - 2 = 26\). Actual third term is 26. This matches.
4. Expected fourth term: \(26 \times 2 - 2 = 52 - 2 = 50\). Actual fourth term is 48. This does not match.

Based on the pattern \(n_{i+1} = n_i \times 2 - 2\), the fourth term should be 50, not 48.

Verifying the Rest of the Series

Let's see if the pattern holds for the subsequent terms if the fourth term was 50.

5. Expected fifth term (starting from the calculated 50): \(50 \times 2 - 2 = 100 - 2 = 98\). Actual fifth term in the series is 98. This matches.
6. Expected sixth term: \(98 \times 2 - 2 = 196 - 2 = 194\). Actual sixth term in the series is 194. This matches.

The pattern \(n_{i+1} = n_i \times 2 - 2\) is consistently followed by all numbers except for 48, which should be 50 to fit the sequence.

Identifying the Incorrect Combination

The number 48 is the one that breaks the established pattern in the series 8, 14, 26, 48, 98, 194. To make the series follow the rule \(n_{i+1} = n_i \times 2 - 2\), 48 should be replaced by 50.

Therefore, the incorrect combination in the given number series is 48.