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Directions to Solve
Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.
Question -
3, 8, 13, 24, 41, ?
  • a)
    70
  • b)
    75
  • c)
    80
  • d)
    85
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Directions to Solve ...
The pattern followed is : nth term + (n + l)th term + (n + 1) = (n + 2)th term.
Thus, 1st term + 2nd term + 2 = 3rd term; 2nd term + 3rd term + 3 = 4th term and so on.
So, missing term = 6th term = 4th term + 5th term + 5 = 24 + 41 + 5 = 70.
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Directions to Solve ...
Pattern Analysis:
To solve this question, we need to identify the pattern in the given series: 3, 8, 13, 24, 41, ?

Pattern Observation:
Let's analyze the given series step by step:
- The difference between the first and second numbers is 8 - 3 = 5.
- The difference between the second and third numbers is 13 - 8 = 5.
- The difference between the third and fourth numbers is 24 - 13 = 11.
- The difference between the fourth and fifth numbers is 41 - 24 = 17.

Pattern Inference:
From the above observations, we can conclude that the differences between the numbers in the series are increasing by 5, then 6, then 7, and so on.

Applying the Pattern to Find the Missing Number:
To find the missing number in the series, we need to continue the pattern of increasing differences.

The difference between the fifth and sixth numbers would be 17 + 8 = 25.

So, if we add 25 to the last number in the given series (41), we get the missing number:
41 + 25 = 66.

Therefore, the missing number in the series is 66.

Verification:
Let's verify our answer by checking if the pattern continues:
- The difference between the fifth and sixth numbers is 66 - 41 = 25.
- The difference between the sixth and seventh numbers is 91 - 66 = 25.

Since the pattern continues, we can conclude that the missing number in the series is indeed 66.

Final Answer:
The correct alternative to replace the question mark in the given series is 70 (option A).
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Question Description
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