# Powers of 3

**Number Theory**Level 2

\[1,3,4,9,10,12,13,\ldots\]

The above sequence consists of the powers of \(3\) or the sum of distinct powers of \(3\), arranged in increasing order.

Find the \(100^\text{th}\) term of the sequence.

\[1,3,4,9,10,12,13,\ldots\]

The above sequence consists of the powers of \(3\) or the sum of distinct powers of \(3\), arranged in increasing order.

Find the \(100^\text{th}\) term of the sequence.

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