Answer:
I guess that the geometric sequence is:
An = 2*5^(n - 2)
we usually have that that a geometric sequence is something like:
A*r^n.
so i will write the first two terms of our sequence separated, and i will calculate the summation of the first seven terms after n = 2.
A0 = 2*5^(-2) = 2/25
A1 = 2*5^-1 = 2/5
Then, the sum for a geometric sequence is:
SN = A(1 - r^N)/(1 - r)
in this case, A = 2 and r = 5, and i will use N = 7 for the sequence 2*5^n
S7 = 2*(1 - 5^7)/(1 - 5) = 39,062.
now we add the first terms that we obtained before and get:
S9 = 2/25 + 2/5 + 39,062 = 39,062.48