What number should replace the question mark in the series 4, 3, 4, 7, 15, ? so that the pattern in the sequence is maintained?

Introduction:
This is a number series problem where you are asked to identify the pattern governing the sequence and then use it to find the missing term. Such questions assess your ability to detect numerical relationships and patterns, which is a key part of logical and quantitative reasoning.

Given Data / Assumptions:

• Series: 4, 3, 4, 7, 15, ?
• We must determine the next term in the sequence.
• Exactly one option continues the logical pattern.

Concept / Approach:
We look for relationships between consecutive terms. Sometimes the pattern involves alternating operations, changing multipliers, or additive sequences. In this case, observing how each term is obtained from the previous one using a combination of multiplication and addition or subtraction reveals a consistent pattern with alternating +1 and −1 and gradually increasing multipliers.

Step-by-Step Solution:
Step 1: Examine consecutive terms:4 → 3, 3 → 4, 4 → 7, 7 → 15.Step 2: Express each step as a multiplication followed by +1 or −1.From 4 to 3: 4 * 1 − 1 = 3.From 3 to 4: 3 * 1 + 1 = 4.From 4 to 7: 4 * 2 − 1 = 7.From 7 to 15: 7 * 2 + 1 = 15.Step 3: Notice the pattern:The multiplier repeats for two steps (1, 1, then 2, 2, then 3, 3, and so on).The sign alternates as −1, +1, −1, +1, etc.Step 4: The next step should use multiplier 3 and sign −1, following the pattern.Step 5: Apply this to the last term: next term = 15 * 3 − 1 = 45 − 1 = 44.

Verification / Alternative check:
Extend the pattern further to test consistency. After 44, the next term would logically be 44 * 3 + 1 = 133, matching the rule of two operations with multiplier 3 and alternating signs. This smooth continuation supports that 44 is the correct missing term.

Why Other Options Are Wrong:
42, 53, and 56 do not fit the described rule of multipliers and alternating plus/minus operations. Plugging any of these into the sequence breaks the consistent pattern. 31 also fails to follow the 3 * 15 ± 1 rule. Only 44 satisfies 15 * 3 − 1 and keeps the pattern intact.

Common Pitfalls:
Students may look only at differences between terms (−1, +1, +3, +8) and not recognize a clear second level pattern. Others may guess based on rough growth trends instead of identifying a precise rule. Always check for combined operations (multiplication plus or minus a constant) and consider repeating structures over pairs of terms.

Final Answer:
The missing term that continues the pattern is 44.