Solve the recurrence relation an = 5an-1 – 6an-2 with initial conditions a0 = 1 and a1 = 2.

Question

Solve the recurrence relation an = 5an-1 &#8211; 6an-2 with initial conditions a0 = 1 and a1 = 2.

Suresh Chand · Accepted Answer

Given recursion relation an = 5an-1 - 6an-2 Here, degree  = 2 Now, the characteristics Equation is r2 = 5r - 6 or, r2 - 5r + 6 = 0 or, (r-2)(r-3) = 0 We get, r = 2,3 Let say r1 = 2 and r2 = 3 Noe, the general solution of the homogeneous equations an = A1r1n + A2 r2n Where, A1 and A2 are scalar or, an = A12n + A23n   ........... (i) Given initial contions a0 = 1 🡲 n = 0 a0 = A120 + A230 or, A1 + A2 = 1  --------- (ii) Also, a1 = 2 🡲 n = 1 a1 = A121 + A231 2A1 + 3A2 = 2  ----------(iii) Solving Equation (ii) and (iii) A2 = 0 and A1 = 1 From Equation, the general solution is an = 2n + 0 × 3n an = 2n

Solve the recurrence relation a_n = 5a_n-1 – 6a_n-2with initial conditions a₀= 1 and a₁= 2.

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Solve the recurrence relation an = 5an-1 – 6an-2 with initial conditions a0 = 1 and a1 = 2.

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Solve the recurrence relation a_n = 5a_n-1 – 6a_n-2with initial conditions a₀= 1 and a₁= 2.