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**Punch** A geometric progression has first term and common ratio both equal to a, a>1. Given that the sum of the first 12 terms is 28 times the sum of the first 6 terms, find the exact value of a.

$\displaystyle S_{12}=28S_6$

$\displaystyle \frac{a(1-r^{12})}{1-r}=28\frac{a(1-r^6)}{1-r}$

$\displaystyle 1-r^{12}=28(1-r^6)$

$\displaystyle r^{12}-28r^6+27=0$

I would have to plot a graph to find the answer, but this would not give me an exact answer. How could I solve it in a way which would give me an exact answer?