What is the sum of the first five terms of a geometric series with a1=6 and r = 1/3

Answer: 14/9

Step-by-step explanation:

Sn = a (1-r^n) / 1-r

S5 = 6 (1 - (1/3) ^5) / 1-1/3

S5 = 6 (1-1/243) / 2/3

S5 = 6 (242/243) / 2/3

S5=6 (242/243) * 3/2

S5=242/27

S5=14/9

Answer: the sum of the first 5 terms is 8.96

Step-by-step 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