Given the geometric sequence where a1 = −3 and the common ratio is 9, what is the domain for n? a) all integers b) all integers where n ≥ −1 c) all integers where n ≥ 1 d) all integers where n ≥ 0

Option C - All integers , where                          

Step-by-step explanation:

Given : The geometric sequence where  and the common ratio is 9,

To find : What is the domain for n?

Solution :

First we form a geometric sequence,

The nth term of geometric sequence is

First term in GP,  

Common ratio, r = 9

Substitute the value,

Now, what you get domain of is all natural numbers e.g., n = {1, 2, 3, ......}

so, domain for n will be all integers where n ≥ 1

Hence, option (C) is correct.

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)