Question

The sum of an infiniteGP is 18. If the first
term is 6, the common ratio is​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Formula used here :

sum of infinity=

$\bold{\red{\boxed{S∞ = \frac{a}{1 - r} }}}$

$= > 18 = \frac{6}{1 - r}$

$= > 6 = 18(1 - r)$

$= >6 = 18 - 18r$

$= 6 - 18 = 18r$

$= > - 12 = 18r$

$= > r = - \frac{12}{18} \: or \: - \frac{2}{3}$

$\bold{Other\: related\: Formulas:}$

Geometric mean between a and b =$\sqrt{ab}$

$\bold{\boxed{r > 1 = \frac{a( {r}^{n} - 1) }{r - 1}}}$

$\bold{\boxed{If \: r < 1 = sn = \frac{a(1 - {r}^{n} )}{1 - r}}}$