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Fantom [35]
3 years ago
10

What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …

Mathematics
1 answer:
MatroZZZ [7]3 years ago
6 0

a_1=-4;\ a_2=-16;\ a_3=-64;\ a_4=-256;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}\to r=\dfrac{-16}{-4}=4

The formula of the sum of a geometric sequence:

S_n=a_1\cdot\dfrac{1-r^n}{1-r}

We have:

a_1=-4;\ n=6;\ r=4

substitute:

S_6=-4\cdot\dfrac{1-4^6}{1-4}=-4\cdot\dfrac{1-4096}{-3}=-4\cdot\dfrac{-4095}{-3}=-4\cdot1365=-5460

Answer: C. -5460

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Step-by-step explanation:

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Answer:

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3 years ago
Solve for x<br> −4(x−7)=36
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Answer:

The answer is 2.0190

Step-by-step explanation:

<em>From the given question,</em>

<em>We recall that,</em>

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<em>so, p = 0.5</em>

<em>The Hypothesis is:</em>

<em>H₀ : P = 0.5, this means that  H0:50% of the games played will be won</em>

<em>vs</em>

<em>H₁ : P > 0.5, This indicates that, win is greater than 0.5 due to home field advantages.</em>

<em>n=241,x=141</em>

<em>Then,</em>

<em>SD(p)=√(p*q/n)=√(0.5*0.5/141)=0.0421</em>

<em>z = p - p/ SD (p) = 0.5850 - 0.5/0.0421 = 0.085/0.0421 =2.0190</em>

<em>therefore, there is strong evidence that there is home field advantages in professional football.</em>

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3 years ago
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= -2

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