Question

The recurrence relation for the solution G(K) =
${5.2}^{k}$
is-​

Answer 1

Given : $G(k)=5.2^k$

To Find :  The recurrence relation for the  

Solution:

$G(k)=5.2^k$

put k = 0

=> G(0) = 5.2⁰  = 5

put k = n - 1

=> G(n-1) = 5 . 2ⁿ⁻¹

put k = n  

=> G(n ) = 5 . 2ⁿ

G(n ) = 5 . 2⁽ⁿ⁻¹⁾⁺¹

=> G(n ) = 5 . 2⁽ⁿ⁻¹⁾ . 2

=> G(n)  = 2. (5 . 2ⁿ⁻¹)

=> G(n) = 2. G(n-1)    where G(0) = 5

=> Gₙ = 2Gₙ₋₁   where G₀ = 5.

The recurrence relation is Gₙ = 2Gₙ₋₁   ,  G₀ = 5.

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