calculus ??

Question

What is the "nth" term of the geometric sequence whose initial term is 4.5 and common ratio is 3?

Thank you for you help!

Answer 1

If we call your INITIAL term A1 then

A1 = 4.5
A2 = 4.5(3)
A3 = 4.5(3^2)
A4 = 4.5(3^3)
A5 = 4.5(3^4)
........
........
An = 4.5[3^(n-1)]
_ _ _ _ _ _ _ _ _ _

However, if you want to call your initial term A0 (which is not the usual start when you're counting terms) THEN

A0 = 4.5 and

An = 4.5[3^n]
_ _ _ _ _ _ _ _

I think the first solution is better.

Answer 2

Since we start at 4.5 we multiply by the common ratio of 3 to get to the next term. So we go from 4.5 to 13.5, 13.5 to 40.5, etc. This means the nth term is

note: a_n means a sub n

So the nth term is:

a_n=4.5(3)^n (it reads a sub n equals 4.5 times 3 to the nth power)


-----------------------------------
Notice if we plug in n=0 we get

a_0=4.5(3)^0=4.5(1)=4.5
If we let n=1
a_1=4.5(3)^1=4.5(3)=13.5
If we let n=2
a_2=4.5(3)^2=4.5(9)=40.5

Answer 3

4.5(3)^n-1
so first term is 4.5(3)^0=4.5*1=4.5
this series diverges

Answer 4

a_n = 4.5 * 3^(n -1), n=1,2,3...