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

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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. Final Answer:105

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

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