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Angelina_Jolie [31]
2 years ago
14

Dan invests £18790 into his bank account. He receives 5.3% per year simple interest. How much will Dan have after 7 years?

Mathematics
1 answer:
Neko [114]2 years ago
8 0

Answer: 55

Step-by-step explanation:

67

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<em>$19.99 x 6 = $119.94</em>

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Calculate the value of x in the equation 2x - 15 =5 - 3×
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\bold{2x - 15 = 5 - 3x} \\  \bold{2x + 3x = 15  +  5} \\  \bold{5x =20 } \\  \bold{x =  \cancel{ \frac {20}{5} }} \\  \bold{x = 4}

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1 year ago
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Find S12 for geometric series: (-7.5) + 15 + (-30) + ...
kolezko [41]

Answer:

S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

Step-by-step explanation:

Given the sequence to find the sum up-to 12 terms

(-7.5) + 15 + (-30) + ...

As we know that

A geometric sequence has a constant ratio 'r' and is defined by

a_n=a_1\cdot r^{n-1}

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

\frac{15}{\left(-7.5\right)}=-2,\:\quad \frac{\left(-30\right)}{15}=-2

\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}

r=-2

\mathrm{The\:first\:element\:of\:the\:sequence\:is}

a_1=\left(-7.5\right)

a_n=a_1\cdot r^{n-1}

\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:

a_n=\left(-7.5\right)\left(-2\right)^{n-1}

a_n=-\left(-2\right)^{n-1}\cdot \:7.5

\mathrm{Geometric\:sequence\:sum\:formula:}

a_1\frac{1-r^n}{1-r}

\mathrm{Plug\:in\:the\:values:}

n=12,\:\spacea_1=\left(-7.5\right),\:\spacer=-2

  =\left(-7.5\right)\frac{1-\left(-2\right)^{12}}{1-\left(-2\right)}

  =-7.5\cdot \frac{1-\left(-2\right)^{12}}{1+2}

\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

  =-\frac{-30712.5}{1+2}          ∵  \left(1-\left(-2\right)^{12}\right)\cdot \:7.5=-30712.5

 =-\frac{-30712.5}{3}

 =\frac{30712.5}{3}

 =10237.5

Thus, S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5        

5 0
3 years ago
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