In a geometric progression, $ S_2 = $ 7 and $ S_6 = $ 91. Assess $ S_4 $. Alternatives: 28, 32, 35, 49, 84.

Here is what I have tried until now:

$$

S_2 = frac {a_1 (1-r ^ 2)} {1-r} implies 1-r = frac {a_1 (1-r ^ 2)} {7} \

S_6 = frac {a_1 (1-r ^ 6)} {1-r} implies 1-r = frac {a_1 (1-r ^ 6)} {91}

$$

Then:

$$

frac {1-r ^ 2} {1} = frac {1-r ^ 6} {13} \

r ^ 6 – 13r ^ 2 + 12 = 0

$$

Now, I can not solve this equation, there may be an easier way …