# How do you find the sum of the infinite geometric series given a_1=12, r=-0.6?

Oct 13, 2017

The sum of the infinite geometric series is $7.50$.

#### Explanation:

Let us consider an infinite geometric series whose first term is ${t}_{1}$ & common multiplier is $r$.

Then,

${t}_{1} = a , {t}_{2} / {t}_{1} = r$.

${S}_{\infty} = \frac{a}{1 - r}$..........(1).

Now given that,

$a = 12$ & $r = - 0.6$

$\therefore r = - \frac{6}{10}$

$\therefore r = - \frac{3}{5}$

Now, applying formula (1) $\rightarrow$

${S}_{\infty} = \frac{12}{1 - \left(- \frac{3}{5}\right)}$

$\therefore {S}_{\infty} = \frac{12}{1 + \frac{3}{5}}$

$\therefore {S}_{\infty} = \frac{12}{\frac{8}{5}}$

$\therefore {S}_{\infty} = \frac{12 \times 5}{8}$

$\therefore {S}_{\infty} = \frac{15}{2}$

$\therefore {S}_{\infty} = 7 \left(\frac{1}{2}\right)$

$\therefore {S}_{\infty} = 7.50$

Therefore, the sum of the infinite geometric series is $7.50$. (Answer).

Hope it Helps:)