Add 1 gallon of water to a tea kettle or sauce pan. Heat to almost boiling. Add 1 cup sugar and stir until dissolved. Remove from heat and add tea bags. Cover and steep for 1 hour.
While waiting for the tea to steep add frozen blackberries to a sauce pan. Add 1 cup water, 2 cups sugar and the lime juice. Bring to a boil (approx 5 minutes). Using a fork mash berries. Don't strain berries.
Once tea has finished steeping pour into tea pitcher. Add tea to 24 oz glass to almost the top of the glass. Pour tea and add 3 tablespoons of the blackberry syrup. Stir well. Serve with a straw for best results.