What is the sum of the first five terms of a geometric series with a1=15 and r=1/3

15, 5, 5/3, 5/9, 5/27

Step-by-step explanation:

Recall, that the general form of a geometric series is

a, ar, ar², ar³, ...

where a is the first term and r is the ratio

It is given that the first time is 15, hence a = 15

also given that ratio is 1/3

hence the first 5 terms are:

15, (15) (1/3), (15) (1/3) ^2, (15) (1/3) ^3, (15) (1/3) ^4

simplifying each term gives

15, 5, 5/3, 5/9, 5/27

605/27 or 22.41 to the nearest hundredth.

Step-by-step explanation:

The formula for the sum of n terms is

an = a1 * (1 - r^n) / (1 - r) where a1 = the first term and r = the common difference.

So here a5 = 15 * (1 - (1/3) ^5) / (1 - 1/3)

= 605/27

= 22.41 to the nearest hundredth.