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2 years ago

11

What is bigger 3.345 or 3.35 or 3.3

1 answer:

Sidana [21]2 years ago

8 0

3.35 is bigger then 3.345

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3 years ago

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MrRa [10]

Answer:

$S_{75}=-506.888989761$ X 10^{32}$

Step-by-step explanation:

Given the sequence

$a_1=-\dfrac{1}{3}\\ a_i=a_{i-1}\cdot (-3)$

$a_2=a_{2-1}\cdot (-3)=a_1 \cdot (-3) = -\dfrac{1}{3}\cdot (-3)=1\\a_3=a_{3-1}\cdot (-3)=a_2 \cdot (-3) = 1 \cdot (-3)=-3\\a_4=a_{4-1}\cdot (-3)=a_3 \cdot (-3) = -3 \cdot (-3)=9\\$

Therefore the sequence is:

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This is a geometric sequence where the:

First Term, $a_1=-\dfrac{1}{3}$

Common ratio, r =-3

We want to determine the sum of the first 75 terms.

For a geometric sequence, the sum:

$S_n=\dfrac{a_1(1-r^n)}{1-r} \\$

Therefore:

$S_{75}=\dfrac{-\dfrac{1}{3}(1-(-3)^{75})}{1-(-3)} \\\\=\dfrac{-(1-(-3)^{75})}{4*3}\\\\S_{75}=\dfrac{(-3)^{75}-1}{12}\\\\S_{75}=-506.888989761$ X 10^{32}$

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3 years ago