If a₁ = 4, a₂ = 6, and aₙ = aₙ₋₁ + aₙ₋₂, what is a₅?
Answer and explanation
Correct answer: 26
The governing concept is a second-order recursive sequence. Every term from the third onward equals the sum of the two terms immediately before it. The initial values are a₁ = 4 and a₂ = 6. Calculate in order: a₃ = a₂ + a₁ = 6 + 4 = 10; a₄ = a₃ + a₂ = 10 + 6 = 16; and a₅ = a₄ + a₃ = 16 + 10 = 26. Hence option C is correct. Option A is the fourth term, so it results from stopping one step too early. Options B and D cannot be obtained by adding the correct pair of preceding terms. The order matters: for a₅, the required pair is a₄ and a₃, not just one earlier term or the original starting values.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The governing concept is a second-order recursive sequence. Every term from the third onward equals the sum of the two terms immediately before it. The initial values are a₁ = 4 and a₂ = 6. Calculate in order: a₃ = a₂ + a₁ = 6 + 4 = 10; a₄ = a₃ + a₂ = 10 + 6 = 16; and a₅ = a₄ + a₃ = 16 + 10 = 26. Hence option C is correct. Option A is the fourth term, so it results from stopping one step too early. Options B and D cannot be obtained by adding the correct pair of preceding terms. The order matters: for a₅, the required pair is a₄ and a₃, not just one earlier term or the original starting values.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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