<u>Given</u>:
The given geometric series is ![2 + 3 + 4.5+ 6.75 + ...](https://tex.z-dn.net/?f=2%20%2B%203%20%2B%204.5%2B%206.75%20%2B%20...)
We need to determine the value of r and a₁
<u>Value of a₁:</u>
The term a₁ denotes the first term of the geometric series.
Hence, from the given series, the first term of the series is 2.
Thus, a₁ = 2.
Therefore, the value of a₁ is 2.
<u>Value of r:</u>
The term r denotes the common ratio between the terms in the geometric series.
The value of r is given by
![r=\frac{3}{2}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B3%7D%7B2%7D%3D1.5)
![r=\frac{4.5}{3}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4.5%7D%7B3%7D%3D1.5)
![r=\frac{6.75}{4.5}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B6.75%7D%7B4.5%7D%3D1.5)
Thus, the value of r is 1.5
Answer:-7
Step-by-step explanation:Let's solve your equation step-by-step.
3(3x+1)−(4x+1)=6x−3(x+4)
Step 1: Simplify both sides of the equation.
3(3x+1)−(4x+1)=6x−3(x+4)
3(3x+1)+−1(4x+1)=6x−3(x+4)(Distribute the Negative Sign)
3(3x+1)+−1(4x)+(−1)(1)=6x−3(x+4)
3(3x+1)+−4x+−1=6x−3(x+4)
(3)(3x)+(3)(1)+−4x+−1=6x+(−3)(x)+(−3)(4)(Distribute)
9x+3+−4x+−1=6x+−3x+−12
(9x+−4x)+(3+−1)=(6x+−3x)+(−12)(Combine Like Terms)
5x+2=3x+−12
5x+2=3x−12
Step 2: Subtract 3x from both sides.
5x+2−3x=3x−12−3x
2x+2=−12
Step 3: Subtract 2 from both sides.
2x+2−2=−12−2
2x=−14
Step 4: Divide both sides by 2.
2x
/2
=
−14
/2
x=−7
(x/6) + 4 = 15
-4 -4
x/6 = 11
x6 . x6
x=66