The topic regarding the number of rak'ahs of Taraweeh can cause quite a bit of debate and confusion, as has occurred in the past, so I think it would be best for you to read the words of the scholars and find your answer there Insha'Allaah. See this thread for some useful links:
What has authentically been reported of the Prophet (sallallaahu 'alayhi wasallam) suggests that there is much flexibility with respect to the number of raka'aat in the salaat al-layl (the night prayer), and they are not restricted to a certain number...