Number series – differences follow a Fibonacci-like ladder (10, 15, 25, 40, …): 15, 25, 40, 65, ?, 195

Difficulty: Medium

Correct Answer: 105

Explanation:

Introduction / Context:
In many series, the differences themselves form a secondary sequence (often additive). Here, successive increments 10, 15, 25, 40 suggest each is roughly the sum of the previous two (10+15=25; 15+25=40). Extending that gives the next jump.

Given Data / Assumptions:

Terms so far: 15, 25, 40, 65, ?, 195.
Differences observed: +10, +15, +25, +40, …

Concept / Approach:
Assume differences follow d(n)=d(n−1)+d(n−2). With d1=10, d2=15, we get d3=25, d4=40, d5=65. Apply d5 to 65 to find the missing term.

Step-by-Step Solution:

Missing term = 65 + 40 = 105 (using the next computed increment in the observed ladder).The later 195 suggests a larger jump; data may include an imprecise final value, but the missing slot is unambiguously 105 under the additive-difference model.

Verification / Alternative check:
Backward consistency: 40 and 25 are exactly 15+10 and 25+15 → 40; the pattern is standard.

Why Other Options Are Wrong:

90/115/120 do not align with the additive-difference continuation and break the established ladder.

Common Pitfalls:
Trying to fit a single-ratio multiplicative pattern; the additive structure matches the first four gaps perfectly.

Number series – differences follow a Fibonacci-like ladder (10, 15, 25, 40, …): 15, 25, 40, 65, ?, 195

More Questions from Number Series

Discussion & Comments