once a week mrs. baxter makes sugar cookies. the first week she makes the recipe, she uses the full 2 cups…

once a week mrs. baxter makes sugar cookies. the first week she makes the recipe, she uses the full 2 cups of sugar it calls for. each week after that, she reduces the amount of sugar by one third. if mrs. baxter became immortal and baked cookies every week for all eternity, how much sugar would she use? round your final answer to the tenths place if necessary. s = type your answer... cups of sugar

once a week mrs. baxter makes sugar cookies. the first week she makes the recipe, she uses the full 2 cups of sugar it calls for. each week after that, she reduces the amount of sugar by one third. if mrs. baxter became immortal and baked cookies every week for all eternity, how much sugar would she use? round your final answer to the tenths place if necessary. s = type your answer... cups of sugar

Answer

Explanation:

Step1: Identify the geometric series parameters

The first term (a = 2) (cups of sugar in the first week). The common ratio (r=\frac{2}{3}) (since she reduces the sugar by one - third each week, so the amount of sugar each week is (\frac{2}{3}) of the previous week's amount).

Step2: Use the formula for the sum of an infinite geometric series

The formula for the sum of an infinite geometric series is (S=\frac{a}{1 - r}), where (|r|\lt1). Substitute (a = 2) and (r=\frac{2}{3}) into the formula: [ \begin{align*} S&=\frac{2}{1-\frac{2}{3}}\ &=\frac{2}{\frac{1}{3}}\ &=2\times3 \end{align*} ]

Answer:

(6) cups of sugar