More and more threes

Algebra Level 4

\[ 3,33,333,\ldots, \underbrace{33333\ldots3}_{n \text{ number of 3's}} \]

Given that the sum of the \(n\) number of terms above is equal to

\[ \frac 1a (b^{n+1} - cn - d ) \]

for positive integers \(a,b,c\) and \(d\). Find the value of \(a+b+c+d+1\).

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