Answer:
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
