write an equation for the nth term of the given geometric sequence.
4, 20, 100...,a(sub)n
a. 100(5)^n-1
b. 4(1/5)^n-1
c. 4(5)^n-1
d. 4(1/5)^n+1

Question

write an equation for the nth term of the given geometric sequence. 
4, 20, 100...,a(sub)n
a. 100(5)^n-1
b. 4(1/5)^n-1
c. 4(5)^n-1
d. 4(1/5)^n+1

btaylor · Answer

you start with 4, then multiply by factors of 5...

anonymous · Answer

thanks BTaylor...any chance you could tell me how you got it?

parthkohli · Answer

You may find that pretty well by checking these:$$ 100(5)^{1 - 1} = 20? $$$$ 4({1 \over 5})^{1 - 1} = 20? $$$$ {4(5)^{1 + 1} = 20?} $$$$4({1 \over 5})^{1 + 1} = 20? $$Continue the process of plugging-in the values till you get the correct choice.

parthkohli · Answer

Let's refer to the formula of the particular GP as 'polynomial'.
So, if n = 1, polynomial = 4.
n = 2, polynomial = 20.
n = 3, polynomial = 100.

parthkohli · Answer

My first reply went wrong :(
Please replace those 20's with 4's.

btaylor · Answer

notice that the exponent is always (n-1). So if n=1, the exponent is 0, and the term is 1. So the coefficient (here, 4 or 100) to that term is a1.

btaylor · Answer

then, the difference is the ratio. Ask yourself, "By what factor is a1 multiplied to get a2?" Here, it is 5. So C is the right answer.

anonymous · Answer

oo okay i see...thanks for all the help guys!!

btaylor · Answer

you're welcome