Question

DIRECTION for the question: In the following question, a series is given with term/s missing. Choose the correct alternative to replace the question mark in the given series.
5, 6, 9, 15, ?, 40

• A. 21
• B. 25
• C. 27
• D. 33
• E. 48

Hint:

In number series problems: • First, always check the difference between consecutive terms. • If the differences don't form a constant sequence, check if the differences themselves form an arithmetic progression (double difference).

Answer 1

The Correct Option is B

Concept:
In a Number Series, the pattern often involves arithmetic operations such as addition of a specific sequence of numbers.
Step 1: Analyze the differences between consecutive terms. The given series is: 5, 6, 9, 15, ?, 40. Difference between 1st and 2nd term: $6 - 5 = 1$ Difference between 2nd and 3rd term: $9 - 6 = 3$ Difference between 3rd and 4th term: $15 - 9 = 6$
Step 2: Identify the pattern in the differences. The differences are 1, 3, 6, ... Notice that the differences themselves form a sequence where their differences are increasing by 1: $3 - 1 = 2$ $6 - 3 = 3$ Therefore, the next difference should be $6 + 4 = 10$. And the difference after that should be $10 + 5 = 15$.
Step 3: Apply the pattern to find the missing term. Add 10 to the 4th term: $15 + 10 = 25$. Check if the pattern holds for the final term: $25 + 15 = 40$. The pattern perfectly matches. \[ \therefore \text{The correct answer is: 25.} \]