Question

Consider the following recursively definef sequence a₀ =3,a₁ =−2,and aₖ​ =2aₖ₋₁​ +aₖ₋​₂ , for every integer k≥2. Then a 4​ =

Answer 1

To find the value of a₄ in the given recursively defined sequence, we can use the formula aₖ = 2aₖ₋₁ + aₖ₋₂. By applying this formula to calculate a₂ and a₃, we can then find a₄ as -9.

Step-by-step explanation:

To find the value of a₄, we will use the recursive definition of the sequence. Given that a₀ = 3 and a₁ = -2, we can calculate a₂ and a₃ as follows:

a₂ = 2a₁ + a₀ = 2*(-2) + 3 = -4 + 3 = -1

a₃ = 2a₂ + a₁ = 2*(-1) + (-2) = -2 - 2 = -4

Finally, we can calculate a₄ using the same formula:

a₄ = 2a₃ + a₂ = 2*(-4) + (-1) = -8 - 1 = -9

Therefore, a₄ = -9.