3 years ago

Mrs Low has some money to buy plates and bowls for her new house.

Mathematics

1 answer:

jekas [21]3 years ago

8 0

Answer:

78=p

$150

$20

6 bowls

Step-by-step explanation:

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A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

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Answer: $\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}$

<u>Step-by-step explanation:</u>

a₁, 375, a₃, a₄, 81

First, let's find the ratio (r). There are three multiple from 375 to 81.

$375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}$

Next, let's find a₁

$a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625$

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

$S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}$