Use proof by mathematical induction to prove explicit formula for recursive sequence is correct

Try using J.G.'s hint and then you can check your answer with the one below.

$P_k = 2 · 3^{k+1} - 14$

Therefore

$P_{k+1} = (2·3^{k+1} - 14)+4.3^{k+1}$

Add the $2·3^{k+1}$ and $4·3^{k+1}$ to get $6·3^{k+1}$

Then

$P_{k+1} = 6·3^{k+1} - 14=2·3^{k+2} - 14$

and you have the correct result.

Tags:

Recursion

Discrete Mathematics

Induction

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