Ahh it's been awhile after I got to know how to solve differentiation problems.. Anyways, I bumped into a few tough questions of arithmetic and geometric sequences.

1. An arithmetic progression has first term a and common difference -1. The sum of the first n terms is equal to the sum of the first 3n terms. Express a in terms of n. (Answer: 2n - 1/2)

2. The sum of the first hundred terms of an arithmetic progression with the first term a and common difference d is T. The sum of the first 50 odd-numbered terms,i.e. the first, third, fifth,.....,ninety-ninth, is 1/2T - 1000. Find the value of d. (Answer: 40)

3. A ball is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing? (Answer: 19m)

From all the questions on arithmetic and geometric progression, I was stuck at these 3 questions... Hope someone can help me out...