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.
1, 3, 4, 8, 15, 27, ?

• A. 37
• B. 44
• C. 50
• D. 55
• E. 95

Hint:

In number series: • When differences don't show a clear pattern, check for additive sequences, where a term is the sum of two or more of its preceding terms.

Answer 1

The Correct Option is C

Concept:
In this Number Series, the pattern is based on the sum of the preceding terms (similar to a Tribonacci sequence).
Step 1: Observe the relationship between consecutive terms. The given series is: 1, 3, 4, 8, 15, 27, ? Let's sum the first few terms to see if they yield the subsequent terms: $1 + 3 + 4 = 8$ (4th term)
Step 2: Verify the pattern for the rest of the series. Sum of 2nd, 3rd, and 4th terms: $3 + 4 + 8 = 15$ (5th term) Sum of 3rd, 4th, and 5th terms: $4 + 8 + 15 = 27$ (6th term) The pattern holds true: each term is the sum of the preceding three terms.
Step 3: Calculate the missing term. Sum of 4th, 5th, and 6th terms: $8 + 15 + 27 = 50$. \[ \therefore \text{The correct answer is: 50.} \]