What is the sum of the first five terms of a geometric series with a1 = 6 and r = 1/3? express your answer as an improper fraction in lowest terms without using spaces.

  242/27

Step-by-step explanation:

Using the formula for the sum, you can fill in the given values and do the arithmetic.

  Sn = a1·(r^n -1)/(r -1)

  S5 = 6·((1/3)^5 -1)/(1/3 -1) = 6(-242/243)/(-2/3) = 6·(121/81)

  S5 = 242/27

Or, you can write the terms and add them up. The sum is ...

  6 + 2 + 2/3 + 2/9 + 2/27 = (162 +54 +18 +6 +2)/27 = 242/27

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls