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Anni [7]
3 years ago
10

What is the sum of the geometric sequence -4, 24, -144, ... if there are 7 terms?

Mathematics
1 answer:
nikdorinn [45]3 years ago
4 0

a_1=-4;\ a_2=24;\ a_3=-144;\ ...\\\\r=\dfrac{a_2}{a_1}\\\\r=\dfrac{24}{-4}=-6

The formula of the sum of a geometric sequence:

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

We have:

a_1=-4;\ r=-6;\ n=7

substitute:

S_7=\dfrac{-4(1-(-6)^7)}{1-(-6)}=\dfrac{-4(1-(-279,936))}{1+6}=\dfrac{-4(1+279,936)}{7}\\\\=\dfrac{-4\cdot279,937}{7}=-159,964

Answer: A: -159,964

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Solve the equation:<br> [3 2<br> 5 5]<br><br> [x1<br> x2]+<br> [1<br> 2]=<br> [2<br> -3]
dsp73

9514 1404 393

Answer:

  (x1, x2) = (3, -4)

Step-by-step explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

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  y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

  (x1, x2) = (3, -4)

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