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

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In summary: It should be an infinite geometric series!In summary, help is needed for the following questions: 1) Finding the sum of the first ten terms of an arithmetic series with the second term being 4.5 and the tenth term being -7.5. 2) Finding the sum to ten terms and the difference between the sum to ten terms and the sum to infinity for a geometric series. 3) Determining the total distance traveled by a ball that is dropped from a height of ten metres and continually bounces back up to a height equal to four-fifths of its previous height. Tips and assistance are welcomed.
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Follz20
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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! :blushing:
 
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  • #2
1) We are given that [itex]a+d=4.5[/itex] and [itex]a+9d=-7.5[/itex] 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?
 

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

1. What is AP and GP?

AP stands for Arithmetic Progression and GP stands for Geometric Progression. They are types of sequences in mathematics where each term is related to the previous one by a common difference or ratio, respectively.

2. How do I find the common difference or ratio in an AP or GP?

To find the common difference in an AP, subtract any term from the term before it. To find the common ratio in a GP, divide any term by the term before it. The resulting value will be the common difference or ratio.

3. What is the formula for finding the nth term in an AP or GP?

The formula for the nth term in an AP is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. The formula for the nth term in a GP is: an = a1r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.

4. How do I determine if a sequence is an AP or GP?

If the difference between consecutive terms is constant, the sequence is an AP. If the ratio between consecutive terms is constant, the sequence is a GP. You can also check by using the formula for the nth term.

5. What are some real-life applications of AP and GP?

AP and GP are used in various fields such as finance, physics, and computer science. In finance, they can be used to calculate interest rates and stock prices. In physics, they can be used to model the motion of objects and calculate their position at different times. In computer science, they can be used in algorithms and data structures to improve efficiency and solve problems.

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