Sums of arithmetic progressions

In summary, we have two questions. The first one asks to find the fourth term of a sequence of partial sums for the given sequence {5+ 3\2 n}. The second question involves a bicycle rider coasting downhill and traveling a certain distance in each second. We are asked to find the total distance traveled in 9 seconds.
  • #1
doreent0722
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1). Find the fourth term of the sequence of partial sums for the given sequence.
{5+ 3\2 n}

2). A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 6 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 9 seconds, find the total distance traveled.

S=________ feet
 
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  • #2
We ask that you post no more than two questions in the initial post of a thread. I have split your latest 4 questions into two threads.

We also ask that you give your thread a title that briefly describes the questions being asked. I have retitled your threads.

And we also ask that when you post questions, you show what you have tried, so we know where you are stuck. Can you show what you've tried for these problems?
 

FAQ: Sums of arithmetic progressions

What is an arithmetic progression?

An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference, denoted by d.

How do you find the sum of an arithmetic progression?

The sum of an arithmetic progression can be found using the formula: S = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference.

Can you give an example of an arithmetic progression?

Yes, an example of an arithmetic progression is: 2, 5, 8, 11, 14, ... where the common difference is 3 and the first term is 2.

What is the difference between an arithmetic progression and a geometric progression?

In an arithmetic progression, the difference between any two consecutive terms is constant, while in a geometric progression, the ratio between any two consecutive terms is constant.

How can arithmetic progressions be applied in real life?

Arithmetic progressions can be applied in many ways, such as calculating interest on a loan, predicting population growth, or analyzing stock market trends.

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