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2 years ago

1/2r + 2 (3/4r - 1) = 1/4r + 6

Mathematics

2 answers:

gtnhenbr [62]2 years ago

7 0

Answer:

r=32/7

Step-by-step explanation:

bazaltina [42]2 years ago

4 0

Let's solve your equation step-by-step.

Step 1: Simplify both sides of the equation.

1/2r + 2 (3/4r - 1) = 1/4r + 6

Step 1: Simplify both sides of the equation.

1/2r + 2 (3/4r - 1) = 1/4r + 6

1/2r+(2)(3/4r)+(2)(-1)=1/4r+6(Distribute)

1/2r+3/2r+-2=1/4r+6

(1/2r+3/2r)+(-2)=1/4r+6(Combine Like Terms)

2r+-2=1/4r+6

2r-2=1/4r+6

Step 2: Subtract 1/4r from both sides.

2r-2-1/4r=14r+6-14r

7/4r-2=6

Step 3: Add 2 to both sides.

7/4r-2+2=6+2

7/4r=8

Step 4: Multiply both sides by 4/7.

(4/7)*(7/4r)=(4/7)*(8)

r=32/7

Answer: r=32/7

hope this helps :)

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The sum of the first 8 terms is 2.51 to the nearest hundredth

Step-by-step explanation:

In the geometric sequence there is a constant ratio between each two consecutive terms

The formula of the sum of n terms of a geometric sequence is:

$S_{n}=\frac{a(1-r^{n})}{1-r}$ , where

a is the first term
r is the constant ratio between the consecutive terms

∵ The sequence is 6 , -5 , 25/6 , .............

∵ -5 ÷ 6 = $\frac{-5}{6}$

∵ $\frac{25}{6}$ ÷ -5 = $\frac{-5}{6}$

- There is a constant ratio between the consecutive terms

∴ The sequence is a geometric sequence

∵ The first term is 6

∴ a = 6

∵ The constant ratio is $\frac{-5}{6}$

∴ r = $\frac{-5}{6}$

∵ We need to find the sum of 8 terms

∴ n = 8

- Substitute the values of a, r and n in the rule above

∴ $S_{8}=\frac{6[1-(\frac{-5}{6})^{8}]}{1-(\frac{-5}{6})}$

∴ $S_{8}=2.511595508$

- Round it to the nearest hundredth

∴ $S_{8}=2.51$

The sum of the first 8 terms is 2.51 to the nearest hundredth

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

3 0

3 years ago

1/2r + 2 (3/4r - 1) = 1/4r + 6​

1/2r + 2 (3/4r - 1) = 1/4r + 6