The sum of the first 3 terms of a geometric progression is 13 times its first term.Find the possible values of the common ratio of the geometric progression.
Hello, mastermin346!
The sum of the first 3 terms of a geometric progression is 13 times its first term.
Find the possible values of the common ratio of the geometric progression.
The first three terms are: .$\displaystyle a,\:ar,\:ar^2$
Their sum is 13 times the first term: .$\displaystyle a + ar + ar^2 \:=\:13a$
We have: .$\displaystyle r^2 + r - 12 \:=\:0 \quad\Rightarrow\quad (r - 3)(r + 4) \:=\:0$
Therefore: .$\displaystyle r \;=\;3\text{ or }-4$