Write a general term formula of the sequence so that the first four terms are 1,4,10,22... (write the verification process)

Write a general term formula of the sequence so that the first four terms are 1,4,10,22... (write the verification process)

a(n)=3*2^(n-1)-2
It is proved that (1) when n = 1, a (1) = 3 * 2 ^ (1-1) - 2 = 1 is in accordance with the proposition
(2) Suppose that a (k) = 3 * 2 ^ (k-1) - 2 holds when n = K
Then a (K + 1) = a (k) * 2 + 2 = 3 * 2 ^ (k) - 2 holds
So it holds for any positive integer n a (n) = 3 * 2 ^ (n-1) - 2

Elden Ring Premiere

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