Could use some help!

Use sigma notation to represent the following series for 9 terms.

Julia bought 7 hats a week later half of all her hats were destroyed in a fire. there are now only 12 hats left with how many did she start

Match the following reasons with the statements given to create the proof. 1. do = ob, ao = oc sas 2. doc = aob given 3. triangle cod congruent to triangle aob vertical angles are equal. 4. 1 = 2, ab = dc if two sides = and ||, then a parallelogram. 5. ab||dc if alternate interior angles =, then lines parallel. 6. abcd is a parallelogram cpcte