What would be the equation and why?

This problem represents a geometric sequence.  Which is always:

a(n)=ar^n where a is the original term, r is the common ratio, and n is the number of terms.

In this case, we wish to know the minimum common ratio which will produce 750000 for the 7th term given that the first term a is  you, one :) so we have the equation...

a(n)=r^n  using 750000 for a(7) and 7 for n...

750000=r^7  taking the natural log of both sides...

ln(750000)=7(lnr)

lnr=ln(750000)/7

r=e^(ln(750000)/7)

r=6.91  since r must be an integer for this particular problem r=7

So our equation was:

a(7)=7^7=823543

note if we only shared with 6 originally you would fall very short...

a(6)=6^7=279936

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