Question

I’m studying geometric sequences and this paper is due tomorrow morning. i barely have any idea what i’m doing. it says to “write the rule for the nth term, then find a7.”

these are the problems

“6, -12, 24, …”

“8, 12, 18, …”

Answer 1

1. -384

2. 91.125 or 91 1/8

Explanation:

formula created by Carl gauss. he's super interesting. if you can read his bio

it's used to figure out stuff like population growth

formula is

an = a1r^n-1

* means multiply

^ means to the power of or exponent

a1 is the first number in the sequence

so 6 times what is -12? -2

-2 will be r

teacher wants a7

so

a7 = 6*-2^7-1

a7 = 6 * -2^6

a7 = 6 * -64

a7 = -384

the next one

to figure out a1

12 ÷ 8 = 1.5

a7 = 8 * 1.5^6

a7 = 91.125 or 91 1/8