Is this cider recipe I made ok?

The following is a cider recipe I made, slightly tweaking a previous one I had. Just curious if this will produce a drink that is safe to drink and won't explode as a bottle bomb or any other crazy thing:

Before you begin make sure everything that will touch your cider is sanitized properly. Not cleaned, sanitized.

ingredients:

• 1 gallon pasteurized apple cider (can use juice if no preservatives)
• 2 cups brown sugar
• 1 packet active dry yeast

• 1 big pot

  Instructions:

• Heat up a little bit of water to recommended temperature on yeast packet to activate yeast. Keep yeast in there for about 15 minutes or until ready to mix with rest of ingredients. Don’t need a lot of water, a quarter of a cup will do.

• Boil 1 cup of water with 1.5-2 cups brown sugar, mix constantly until everything is dissolved. Keep boiling for at least 2-3 minutes.
• Turn off heat.
• Mix syrup and apple juice/cider first so temperature of your sugar mix/syrup is lowered and doesn’t kill yeast
• Add yeast to mixture
• Stir a lot to add oxygen into the mix
• Put into gallon jug and add airlock. I personally put a plug on top that has a hole for hose attachment, and then make hose go into a Glass of water that is 75% filled with water
• Wait 1 week
• Boil .5 cups water with 2 tablespoons brown sugar. Make into syrup like before and wait until a lot of the water has evaporated and you are left with a syrup.
• Siphon cider out cider into large pot and add the syrup you just made
• Put everything into bottles. Grolsch bottles with flip cap work well here.
• Wait 1 week and put in fridge.
• Enjoy a cold one!