Question

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

Answer 1

Answer: 1) D 2). B

Explanation:

Answer 2

1) All integers where n ≥ 1

2) -1,023

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`