# sequences and series – In a geometric progression, \$ S_2 = \$ 7 and \$ S_6 = \$ 91. Estimate \$ S_4 \$.

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 …