The sum of the first three terms of a Geometric Progression (GP) is 14. If the first term is 2, find the first five terms, given that the common ratio is positive.

For this I wrote:

$2 + 2r + 2r^2 = 14$

meaning that $r$ is a root of the quadratic equation $ r^2 + r - 6 = 0.$

From which I obtained values of $r$ at $2$ or $-3$ with the negative value inapplicable. Furthermore I obtained value for the sum of the first five terms is $62$.

My manual states that the two possible sums of the first five terms are $10$ or $62$ ; I am unable to reach the value $10$.

  • $\begingroup$ $$2+2r+2r^2=14\iff r^2+r-6=0$$ $\endgroup$ – lab bhattacharjee Aug 20 '16 at 8:57
  • $\begingroup$ This is what I actually meant, thanks though $\endgroup$ – user362532 Aug 20 '16 at 8:59

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