Question
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  1. The sum of the lirst 5 ferms of an arithmetic sequence is 0 and the fifth term is 8 . Determin
    contmond diference and the first term.
  2. In a geonetific series the first term is 36 , the last term is 16 and the sum of the series is 76 .
    Determine the coinmon ratio and the number of terns in the sequence.

Ask by Medina Barber. in South Africa
Jan 05,2025

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Tutor-Verified Answer

Answer

Problem 4:
  • First term ( ):
  • Common difference ( ):
Problem 5:
  • Common ratio ( ):
  • Number of terms ( ):

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Beyond the Answer

In an arithmetic sequence, if the sum of the first five terms is zero and the fifth term is 8, you can set up some equations. The fifth term is given by (where is the first term and is the common difference). The sum of the first five terms can be expressed as . Solving this system of equations gives you the values for and as and respectively.
For the geometric series where the first term is 36, the last term is 16, and the sum of the series is 76, you can use the formula for the sum of a geometric series . Here, you can set up equations involving , , and to solve for the common ratio and the number of terms . After some manipulations, you find is approximately and is 5.

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