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S4 = 270

Step-by-step explanation:

The 4th partial sum of the sequence is the sum of the first 4 terms:

S4 = a(1) + a(2) + a(3) + a(4)

Because the sequence is geometric any term can be written in terms of the previous one:

a(n) = r a(n - 1)

And more importantly in terms of the first term a(1) so that

a(2) = r a(1)

a(3) = r a(2) = r^2 a(1)

a(4) = r a (3) = r^3 a(1)

Then the 4th partial sum is

S4 = a(1) + r a(1) + r^2 a(1) + r^3 a(1)

S4 = a(1) (1 + r + r^2 + r^3)

With a a(1) = 18 and r = 2 we have

S4 = 18 (1 + 2 + 4 + 8) = 270

Therefore, the 4th partial sum is 270