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Difficult

Ratio From Two Different Series

ALGEBR-8VTTXM

The value of an infinite geometric series is:

$$\sum_{n=1}^{\infty}a_n=52$$

...and the sum of the even terms of the same sequence is $\cfrac{52}{3}$. What is the common ratio of the original sequence?

A

$r_a=\cfrac{1}{2}$

B

$r_a=\cfrac{1}{3}$

C

$r_a=\cfrac{1}{4}$

D

$2$

E

None of the above