Mathematics: The sum of the second and third terms of a geometric sequence is 96. The sum to infinity of this sequence is 500. Find the possible values for the common ratio, r.

The sum of the second and third terms of a geometric

Fangflora3

03.02.2022

Let, first term be a and common ratio is r.

So, $\dfrac{a}{r}+\dfrac{a}{r^2}=96$

Sum of series, $S = \dfrac{a}{1-r}=500$

a = 500( 1 - r )

$a( \dfrac{1}{r}+\dfrac{1}{r^2})=96\\\\r=0.916$

Therefore, the value of common ratio is 0.916 .

Hence, this is the required solution.

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