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jonny [76]
2 years ago
7

How do you rewrite 6/9 in two different ways

Mathematics
1 answer:
Naya [18.7K]2 years ago
4 0

We have to represent the fraction \frac{6}{9} in two different ways.

Let us multiply the numerator and denominator of the given fraction by '2'.

Therefore, \frac{6}{9} = \frac{6 \times 2}{9 \times 2} = \frac{12}{18}

Therefore, \frac{12}{18} is the first way to represent the given fraction.

Now, Let us multiply the numerator and denominator of the given fraction by '3'.

Therefore, \frac{6}{9} = \frac{6 \times 3}{9 \times 3} = \frac{18}{27}

Therefore, \frac{18}{27} is the second way to represent the given fraction.

Therefore,  \frac{12}{18} and  \frac{18}{27} are the different ways to represent the fraction \frac{6}{9}.

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In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the
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Answer:

the common ratio is either 2 or -2.

the sum of the first 7 terms is then either 765 or 255

Step-by-step explanation:

a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.

so,

a1

a2 = a1×f

a3 = a2×f = a1×f²

a4 = a3×f = a1×f³

the problem description here tells us

a3 = 4×a1

and from above we know a3 = a1×f².

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and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).

again, the problem description tells us

a2 + a4 = 30

a1×f + a1×f³ = 30

for f = 2

a1×2 + a1×2³ = 30

2a1 + 8a1 = 30

10a1 = 30

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for f = -2

a1×-2 + a1×(-2)³ = 30

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the sum of the first n terms of a geometric sequence is

sn = a1×(1 - f^(n+1))/(1-f) for f <>1

so, for f = 2

s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765

for f = -2

s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =

= -1×-255 = 255

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