Question
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The second term of a geometric sequence is 6 and the fourth term is 5
Find the sums of two possible series to 20 terms.

Ask by Beck Stanley. in South Africa
Jan 27,2025

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Answer

The sums of the two possible 20-term geometric series are approximately 63.4 and –2.88.

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Mind Expander

To solve the problem, we first notice that in a geometric sequence, each term can be represented as , where is the first term and is the common ratio. Given the second term is 6, we have , and for the fourth term being 5, we have .
By dividing the equations, we can find :
Using values, we can find . For :
gives .
For :
gives .
Now we have two possible series. The sum of the first terms of a geometric series is given by:
Calculating :
  1. For :
  2. For :
Both calculations will yield the sums for the two possible series to 20 terms.

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