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4 years ago

What is the sum of the geometric sequence 3,12,48... if there are 8 terms?

Mathematics

1 answer:

s344n2d4d5 [400]4 years ago

6 0

Answer:

C) 65,535

Step-by-step explanation:

You can add up the 8 terms ...

3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

<em>Estimating</em>

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

<em>Using the formula</em>

You know the formula for the sum of a geometric sequence is ...

S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

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Ahmed and Gavin are playing both chess and checkers. The probability of Ahmed winning the chess games is 45%. The probability of

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Answer:

Option A. Ahmed wins the chess game

Step-by-step explanation:

we know that

The probability of Ahmed winning the chess games is 45%

45%=045/100=0.45

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Compare the probability

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4 years ago

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Answer:

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3 years ago

Pls help pls show working brainliest given to clearest answer

myrzilka [38]

Answer:

$x_1=\frac{1+\sqrt{61}}{6}\approx1.47,x_2=\frac{1-\sqrt{61}}{6}\approx-1.14$

Step-by-step explanation:

To solve a non-factorable quadratic equation in the form of $ax^2+bx+c=0$ , you need to use the quadratic formula where $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ :

$3x^2+x-5=0$

$x=\frac{-1\pm\sqrt{1^2-4(3)(-5)}}{2(3)}$

$x=\frac{-1\pm\sqrt{1+60}}{6}$

$x=\frac{-1\pm\sqrt{61}}{6}$

Because of the $\pm$ sign, quadratic equations always have two solutions, whether both are real, only one is real, or both are complex (in the form of $a+bi$ where $a$ is the real part and $b$ is the imaginary part where $i=\sqrt{-1}$ ). In this case, because the discriminant is positive (defined as $b^2-4ac$ ), then there are 2 real solutions.