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**GGC4** The arithmetic series I have begins with 100, and increases in increments of 100. (so d=100, a1=100, a2=200, a3=300, etc)

The geometric series I have begins with 2 and increases in increments of 2. so r=2, a1=2, a2=4, a3=8, etc.)

I know the formulas an=d(n-1) + a1

and an=a1r^n-1

...but I don't know how to apply them to find at what term n the two series will meet.

Help, please?

Let's call the first series $\displaystyle a_n$ and the second series $\displaystyle b_n$. We want to find $\displaystyle n$ such that $\displaystyle a_n=b_n$.

$\displaystyle a_n = d(n-1)+a_1 = 100(n-1)+100 = 100n - 100 + 100 = 100n$

$\displaystyle b_n = b_1r^{n-1} = 2\cdot 2^{n-1} = 2^{n-1+1} = 2^n $

Solve for $\displaystyle n$:

$\displaystyle \fbox{100n=2^n}$