Sums of arithmetic progressions

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SUMMARY

The discussion focuses on solving problems related to sums of arithmetic progressions. The first problem involves finding the fourth term of the sequence of partial sums for the series defined by the formula {5 + 3/2 n}. The second problem calculates the total distance traveled by a bicycle rider who starts at 7 feet in the first second and increases his distance by 6 feet each subsequent second, reaching the bottom of the hill in 9 seconds. Participants are encouraged to demonstrate their attempts at solving these problems to facilitate better assistance.

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  • Understanding of arithmetic progressions and their properties
  • Basic knowledge of sequences and series
  • Familiarity with algebraic manipulation and summation formulas
  • Ability to apply mathematical reasoning to real-world scenarios
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  • Study the formula for the sum of an arithmetic series
  • Learn how to derive the nth term of an arithmetic progression
  • Explore the concept of partial sums in sequences
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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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