Question

Find the sum of this infinite geometric series where a1=0.3 and r=0.55

Answer 1

Hello, Marymack!


We know that in a geometric sequence defined by $\mathsf{a_1}$ and $\mathsf{r}$ , the sum can be calculated the following way:

$\mathsf{S_n = \dfrac{a_1}{1-r}}\\ \\ \\ \\ \mathsf{S_n = \dfrac{0.3}{1-0.55}}\\ \\ \\ \mathsf{S_n = \dfrac{0.3}{0.45}}\\ \\ \\ \boxed{\mathsf{S_n = \dfrac{2}{3}=0.666...}}$

Answer 2

Answer:

The sum of the infinite geometric sequence is given by:

$S_{\infty} = \frac{a_1}{1-r}$          ....[1]

where,

$a_1$ is the first term

r is the common ratio.

As per the statement:

Given that $a_1 = 0.3$ and r = 0.55

To find the sum of this infinite geometric series.

Substitute the given values in [1] we have;

$S_{\infty} = \frac{0.3}{1-0.55}$

⇒$S_{\infty} = \frac{0.3}{0.45}$

Simplify:

$S_{\infty} \approx 0.67$

Therefore,  the sum of this infinite geometric series approximate is, 0.67