What are some helpful tips for solving AP & GP questions?

[Follz20]

Hi all. Any help on these annoying questions will be much appreciated!

1) The second term of an AP is 4.5 and the tenth term is -7.5. Find the sum of the first ten terms.

2) For the series √2 + 1 + 1/√2 + ...

a) Find the sum to ten terms of the series
b) what is the difference between the sum to ten terms and the sum to infinity?

3) A ball is dropped from a height of ten metres. It continually bounces back up to a height equal to four-fifths of its previous height. Find the total distance traveled by the ball.

I am quite bad at this so any help or tips from anyone will be gladly accepted! Cheers!

 

[Mentallic]

1) We are given that $a+d=4.5$ and $a+9d=-7.5$ where a is the first term and d is the difference between each term. Solve these 2 equations simultaneously and then plug your results into your sum of an arithmetic formula.

2)
a)What is the ratio between each term? This should be enough to simply plug into your geometric summation formula!
b)The same deal, just use your sum to infinite of a geometric series formula and then it's obvious from there.

3)Can you create a summation series to describe the distances the ball is travelling?