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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?

 Dec 25, 2021
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F  +  FR ==7,               

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

 

Use elimination and factorization to get:

 

F ==7/2 * (sqrt(3 - 1)  or: - 7/2 * (1 + sqrt(3)) - this is the first term [you have 2 solutions]

R ==sqrt(3) 0r: - sqrt(3) - this is the common ratio. [again, you have 2 solutions]

 

2.562177826 , 4.437822174 , 7.686533479 , 13.31346652 , >>Number of terms = 4>>Total Sum == 28

 Dec 25, 2021

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