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In a geometric sequence of real numbers, the sum of the first 2 terms is 7, and the sum of the first 6 terms is 91. What is the sum of the first 4 terms?

 Apr 4, 2022
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7==F * [1 - R^2] / [1 - R],   

91==F * [1 - R^6] / [1 - R], solve for F, R

 

Use division to get:

F ==2.56218- this is the first term

R==1.73205 - this is the common ratio==sqrt(3)

 

Sum of the first 4 terms==[2.56218 * [1 - sqrt(3)^4] / [1 - sqrt(3) ]==28

 Apr 4, 2022

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