The sum of the second and third terms of a geometric sequence is 96. The sum to infinity of this sequence is 500. Find the possible values for the common ratio, r.
2026-03-24 22:08:21.1774390101
Find the possible values for the common ratio, r.
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$ar+ar^2=96$, $\frac{a}{1-r}$=500.
$ar(1+r)=96, a=500(1-r)$
$500(1-r)r(1+r)=96, r-r^3=\frac{96}{500}$ now i think you can calculate this by your own.. $r=\frac{1}{5}, \frac{\sqrt{97}-1}{10}, \frac{-\sqrt{97}-1}{10}$