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1 year ago

THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2

Mathematics

1 answer:

zhuklara [117]1 year ago

6 0

Answer:

a = 150

Step-by-step explanation:

Sum to infinity of a geometric series

$S_{\infty}=\dfrac{a}{1-r}\:\textsf{ for }|r| < 1$

where:

a is the first term
r is the common ratio

Given:

$S_{\infty}=100$

$r=-\dfrac{1}{2}$

Substitute the given values into the formula and solve for a:

$\begin{aligned}S_{\infty} & =\dfrac{a}{1-r}\\\\\implies 100 & =\dfrac{a}{1-\left(-\frac{1}{2}\right)}\\\\ 100 & =\dfrac{a}{1+\frac{1}{2}}\\\\100 & = \dfrac{a}{\frac{3}{2}}\\\\a & = \dfrac{3}{2} \cdot 100\\\\a & = 150\end{aligned}$

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The answer is: [C]: " f(c) = $\frac{9}{5}$ c + 32 " .
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Explanation:
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Given the original function:

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→ Write the original function as: " y = (5/9) (x − 32) " ;

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→ That is, solve this equation for "y" ; with "c" as an "isolated variable" on the
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_____________________________________________________

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__________________________________________

As such:
__________________________________________

" ( $\frac{5}{9}$ ) * (y − 32) " ;

= [ ( $\frac{5}{9}$ ) * y ] − [ ( $\frac{5}{9}$ ) * (32) ] ;

= [ ( $\frac{5}{9}$ ) y ] − [ ( $\frac{5}{9}$ ) * ( $\frac{32}{1})$ " ;

= [ ( $\frac{5}{9}$ ) y ] − [ ( $\frac{(5*32)}{(9*1)}$ ] ;

= [ ( $\frac{5}{9}$ ) y ] − [ ( $\frac{(160)}{(9)}$ ] ;

= [ ( $\frac{5y}{9}$ ) ] − [ ( $\frac{(160)}{(9)}$ ] ;

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_______________________________________________
And rewrite as:

→ " x = $\frac{(5y-160)}{9}$ " ;

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→ " x = $\frac{(5y-160)}{9}$ " ;

↔ " $\frac{(5y-160)}{9}$ = x ;

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_______________________________________________________

→ 5y − 160 + 160 = 9x + 160 ;

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→ y = (9/5)x + 32 ;

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Note that "x = c" ;
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So, the inverse function is: " f(c) = (9/5) c + 32 " .
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The answer is: " f(c) = $\frac{9}{5}$ c + 32 " ;
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→ which is:

→ Answer choice: [C]: " f(c) = $\frac{9}{5}$ c + 32 " .
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THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2​

THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2