$\frac{16}{48}=\\\\\frac{16:2}{48:2}=\boxed{\frac{8}{24}}\\\\\frac{8:2}{24:2}=\boxed{\frac{4}{12}}\\\\\frac{4:2}{12:2}=\boxed{\frac{2}{6}}\\\\\frac{2:2}{6:2}=\boxed{\frac{1}{3}}\\\\\frac{1\cdot10}{3\cdot10}=\boxed{\frac{10}{30}}\\\vdots$

6 0

3 years ago

Please explain every step

pogonyaev

<h3>Answer:</h3>

761680

<h3>Explanation:</h3>

$\sf \boxed{\sum _{n=1}^{44}\:60\left(1.2\right)^{n-2}}$

<u>Identify the following's</u>:

First Term [a] = 60(1.2)ⁿ⁻² = 60(1.2)¹⁻² = 50

Common ratio [r] = 1.2

Total Terms [n] = 44

===========================

$\sf Geometric \ Sum \ of \ Terms = \dfrac{a(r^n - 1)}{r-1}$

===========================

Solving Steps:

<em /> $\rightarrow \sf \dfrac{a(r^n - 1)}{r-1}$ <em />

<em />

<em /> $\rightarrow \sf \dfrac{50(1.2^{44} - 1)}{1.2-1}$ <em />

<em />

<em /> $\rightarrow \sf 761679.5808$ <em />

<em />

$\rightarrow \sf 761680 \ \ \ (rounded \ to \ nearest \ integer)$

8 0

2 years ago