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

Hello, Marymack!

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

[tex]\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...}}[/tex]

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OrethaWilkison OrethaWilkison · Answer 2 · 2019-05-27T19:18:26+02:00

Answer:

The sum of the infinite geometric sequence is given by:

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

where,

[tex]a_1[/tex] is the first term

r is the common ratio.

As per the statement:

Given that [tex]a_1 = 0.3[/tex] and r = 0.55

To find the sum of this infinite geometric series.

Substitute the given values in [1] we have;

[tex]S_{\infty} = \frac{0.3}{1-0.55}[/tex]

⇒[tex]S_{\infty} = \frac{0.3}{0.45}[/tex]

Simplify:

[tex]S_{\infty} \approx 0.67[/tex]

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