Answer: the sum of the first 5 terms is 8.96
Explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
a = 6
r = 1/3
n = 5
Therefore, the sum of the first 5 terms, S5 is
S5 = 6(1 - 1/3^5)/(1 - 1/3)
S5 = 6(1 - 1/243)/(2/3)
S5 = 6(242/243)/(2/3)
S5 = (1452/243)/(2/3)
S5 = (1452/243) × (3/2)
S5 = 4356/486
S5 = 8.96