Question 23

Given the geometric sequence where a1 = 1 and the common ratio is 6, what is the domain for n?

A) All integers where n ≥ 1

B) All integers

C) All integers where n ≥ −1

D) All integers where n ≥ 0

Question 24

Find the sum of a finite geometric sequence from n = 1 to n = 5, using the expression −3(4)n − 1.

A) -1,023

B) 1,223

C) 1,023

D) −4,374

Question

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Respuesta :

haleyfordice75 haleyfordice75 · Answer 1 · 2019-04-10T15:42:58+02:00

Answer: 1) D 2). B

Step-by-step explanation:

Answer Link

wifilethbridge wifilethbridge · Answer 2 · 2019-05-07T07:11:01+02:00

Answer:

1) All integers where n ≥ 1

2) -1,023

Step-by-step explanation:

We are given a G.P. where

First term = [tex]a_1=1[/tex]

Common ratio = r = 6

nth term of G.P. = [tex]a_n=ar^{n-1}[/tex]

where a is the first term

So, Substitute n = 1

[tex]a_1=(1) 6^{1-1}[/tex]

[tex]a_1=1[/tex]

So, Domain for n = All integers where n ≥ 1

Now Find the sum of a finite geometric sequence from n = 1 to n = 5, using the expression [tex]-3(4)^{n-1}[/tex]

[tex]\sum^{n=5}_{n=1} -3(4)^{n-1}[/tex]

[tex] -3(4)^{1-1}+(-3(4)^{2-1})+(-3(4)^{3-1})+(-3(4)^{4-1})+(-3(4)^{5-1})[/tex]

[tex] -3-12-48-192-768[/tex]

[tex] -1023[/tex]