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

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 420 People

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

Answered by maham237 @ 22/12/2020

Answer:

1) All integers where n ≥ 1

2) -1,023

Step-by-step explanation:

We are given a G.P. where

First term = $a_1=1$

Common ratio = r = 6

nth term of G.P. = $a_n=ar^{n-1}$

where a is the first term

So, Substitute n = 1

$a_1=(1) 6^{1-1}$

$a_1=1$

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 $-3(4)^{n-1}$

$\sum^{n=5}_{n=1} -3(4)^{n-1}$

$-3(4)^{1-1}+(-3(4)^{2-1})+(-3(4)^{3-1})+(-3(4)^{4-1})+(-3(4)^{5-1})$

$-3-12-48-192-768$

$-1023$

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