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777dan777 [17]
3 years ago
9

Which expression could be used to find the sum of the first n terms of the geometric sequence that begins 11,22,44,…?

Mathematics
1 answer:
REY [17]3 years ago
5 0
= 11( - 1)
Step-by-step explanation:
The sum to n terms of a geometric sequence is
=
where a₁ is the first term and r the common ratio
Here a₁ = 11 and r = = = 2 , then
= = 11 ( - 1)
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Answer:

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore,  x + y : x - y= 3 : 2 is proved.

Step-by-step explanation:

Given

x + y : x - y = 3 : 2

As

x + y = 3

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Solving to find x and y

\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}

x-y=2

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\underline{x+y=3}

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\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}

solve for y

-2y=-1

Divide both sides by 2

\frac{-2y}{-2}=\frac{-1}{-2}

y=\frac{1}{2}

\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=\frac{1}{2}

x+\frac{1}{2}=3

x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}

x=\frac{5}{2}

so

x=\frac{5}{2},\:y=\frac{1}{2}

Thus,

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore,  x + y : x - y= 3 : 2 is proved.

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