Geometric Progression nth Term: Formula and Working Example

[ghostbuster25]

just a check of my work please.

I have to write an expression for the nth term of this geometric sequence.

a₁=100
a₂=106
a₃=112.36

I've worked out the ratio to be r=1.06

I am using the formula u_n=ar^(n-1)

so the expression i have come up with is u_n=100(1.06)^(n-1)

Is this correct? I have checked and it does work. I tried multiplying 100(1.06) on its own first to give me the formula
106^(n-1)
but that doesn't work...hence me doubting myself.

Any comments much appreciated

 

[tiny-tim]

hi ghostbuster25!

… so the expression i have come up with is u_n=100(1.06)^(n-1)

Is this correct? I have checked and it does work. I tried multiplying 100(1.06) on its own first to give me the formula
106^(n-1)
but that doesn't work...hence me doubting myself.

yup, u_n=100(1.06)^(n-1) is fine

(i don't understand how you got 106^(n-1) )

 

[Mentallic]

ghostbuster, if what you were trying to do is convert 100(1.06)^{n-1} into 106^{n-2}, this is wrong because what you should be doing is taking out the factor of 1.06 to give 100(1.06)(1.06)^{(n-1)-1}=106(1.06)^{n-2}.

106ⁿ grows much faster than 1.06ⁿ.