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 $10$.