Root Category (id: 1)
 - Apparel (id: 2)
   -- Shirts (id:4)
   -- Pants  (id:5)
 - Accessories (id: 3)
   -- Handbags (id:6)
   -- Jewelry (id:7)
On Magento we can get the category Ids of a product by using $productObj->getCategoryIds() 
$productObj = Mage::getModel('catalog/product')->load($product_id);
$categoryIds =  $productObj->getCategoryIds();
Which will return an array of category Ids of the product. I have a specific need to get the first level parent of category of a product. Takes for example the category tree above, if a product is categorized in Pants category, I want to get the first level category which is Apparel (in this case, the product only tagged under Pants category but not tagged in Apparel category).
Question: what method can I use to get the parent category of a sub category, or is it possible to get the first level category from a product?
You can use the catalog/category model and its method getParentCategory():
foreach ($categoryIds as $iCategoryId) {
    $m = Mage::getModel('catalog/category')
        ->load($iCategoryId)
        ->getParentCategory();
    var_dump($m->debug());
}
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