Question

Find the general term a_n for the geometric sequence a_1 = -3 and a_2 = 12

Answer 1

you have the first term, and that is a_1 = -3

Answer 2

you need the common ratio now

that's just

r = (second term)/(first term)

r = (a_2)/(a_1)

r = (12)/(-3)

r = -4

Answer 3

you now know the first term is

a_1 = -3

and the common ratio is

r = -4

Answer 4

put this all together to get this nth term formula

a_n = (a_1)*(r)^(n-1)

a_n = -3*(-4)^(n-1)

and that's all there is to it

Answer 5

is it n minus 1 or is it n = -1
I am sorry I'm still a little lost this isn't my best subject

Answer 6

it's n-1

Answer 7

the reason it's not just 'n' is because if you start at n = 1, then you have to shift from 'n' to n - 1

Answer 8

so the formula in a better view is

\[\Large a_{n} = -3(-4)^{n-1}\]

Answer 9

oh ok thats better I was getting confused now I understand it thank you

Answer 10

Notice how if n = 1 (first term), then...

\[\Large a_{n} = -3(-4)^{n-1}\]

\[\Large a_{1} = -3(-4)^{1-1}\]

\[\Large a_{1} = -3(-4)^{0}\]

\[\Large a_{1} = -3(1)\]

\[\Large a_{1} = -3\]

which is the first term given above

You can do the same for n = 2 to find that a_2 = 12

Answer 11

thank you so much

Answer 12

you're welcome