Question

A sequence is defined recursively. Find the first seven terms of the sequence. aₙ = aₙ₋₁ + 2aₙ₋₂, a₁ = 1 , a₂ = 3

Answer 1

The first seven terms of the given sequence, defined recursively as aₙ = aₙ₋₁ + 2aₙ₋₂, are 1, 3, 5, 11, 21, 43, 85.

Step-by-step explanation:

The given sequence is defined recursively as aₙ = aₙ₋₁ + 2aₙ₋₂. The initial terms are a₁ = 1 and a₂ = 3. We can use these initial conditions to find the first few terms of the sequence.

1. a₁ = 1
2. a₂ = 3
3. a₃ = a₂ + 2a₁ = 3 + 2(1) = 5
4. a₄ = a₃ + 2a₂ = 5 + 2(3) = 11
5. a₅ = a₄ + 2a₃ = 11 + 2(5) = 21
6. a₆ = a₅ + 2a₄ = 21 + 2(11) = 43
7. a₇ = a₆ + 2a₅ = 43 + 2(21) = 85

Therefore, the first seven terms of the sequence are 1, 3, 5, 11, 21, 43, 85.