Question

We know that the first term is 6 and the fifth term is 96. We also know that n = 5.
We need to find the common ratio or r.

tn = t1rn-1

96 = 6r5-1

96 = 6r^4

r^4 = 16

r = ±2

please help I don't know where the 6 goes and why it becomes 16

Answer 1

96 = 6r^4

Answer 2

okay I understand that 96/6 is 16

Answer 3

so r^4 = 16
or r^4 =2^4

Answer 4

after the 16, why does it become two?

Answer 5

16 =2*2*2*2 = 2^4

Answer 6

It's the fourth root of 16

Answer 7

OHHHHHHHokay!

Answer 8

wait no nvm

Answer 9

r=2 and since its to the fourth power, it can also be negative

Answer 10

hold on

Answer 11

but why does r=2 that part isn't clicking for me.

Answer 12

The fourth root of 16=2

Answer 13

2^4=16

Answer 14

2*2*2*2 = 2^4
so
r^4 =2^4
so we can say
(r/2)^4 =1

now if (r/2) is 1 then it will result in one if raised to power of 4
so r/2=1
so r=2

Answer 15

But ^4 is even so it can be negative 2 as well

Answer 16

so it's just something that would go into it??

Answer 17

similarly
one can argue
r^4 =(-2)^4 so r can be -2

Answer 18

Yes, it is a variable this means if we plugged in r=2
2^4=16, 16=16 it is true
(-2)^4=16, 16=16 is true
that means r=2 or -2

Answer 19

suppose
3^2 = 9
and now if i ask
(x)^2 =9 can you guess what x can be

Answer 20

okay okay okay! i looked at more of my notes and it explained it! thank you!!!

Answer 21

3 :)

Answer 22

yup

Answer 23

i hope y get it now