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

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

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!