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Soru

Zorluk: OrtaNumber and Alphabet Series

In the following number sequence, a specific mathematical pattern is followed:

7,14,25,42,67,?7, 14, 25, 42, 67, ?

What is the value of the missing term represented by the question mark?

Cevap: 102

Cevap

The missing term in the series is 102.
The correct answer is 102. The sequence is governed by a double difference pattern. The consecutive differences between terms are 7, 11, 17, and 25. The differences of these differences are 4, 6, and 8, which increase by 2 at each step. Thus, the next second difference is 10, the next term difference is 35, and the next term in the sequence is 67 + 35 = 102.

Adım Adım Çözüm

1
Find the first-order differences between consecutive terms.
The differences are 7, 11, 17, and 25.
Analyzing first differences helps determine if the growth rate follows a recognizable secondary pattern.
2
Find the second-order differences.
The differences between the consecutive first differences are 4, 6, and 8.
Since the first differences are non-linear, second-order differences reveal the underlying constant acceleration (+2).
3
Project the next first-order difference using the second-order pattern.
The next second-order difference is 10 (since 8 + 2 = 10), making the next first-order difference 25 + 10 = 35.
Extrapolating the arithmetic pattern of the second differences yields the correct next increment.
4
Add the projected difference to the last term of the sequence.
67 + 35 = 102.
Applying the calculated increment to the last term completes the series.

Anahtar Kavram

Second-order arithmetic sequence (Double Difference Series)
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Konular

Number and Alphabet Series

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