Given:
The sum of two terms of GP is 6 and that of first four terms is 
To find:
The sum of first six terms.
Solution:
We have,


Sum of first n terms of a GP is
...(i)
Putting n=2, we get


...(ii)
Putting n=4, we get



(Using (ii))
Divide both sides by 6.
Taking square root on both sides, we get

Case 1: If r is positive, then using (ii) we get
The sum of first 6 terms is




Case 2: If r is negative, then using (ii) we get
The sum of first 6 terms is




Therefore, the sum of the first six terms is 7.875.
3x _> 3.0 - 2.4
= 3x _> 3/5
= 1/5
well, let's first notice, all our dimensions or measures must be using the same unit, so could convert the height to liters or the liters to centimeters, well hmm let's convert the volume of 1000 litres to cubic centimeters, keeping in mind that there are 1000 cm³ in 1 litre.
well, 1000 * 1000 = 1,000,000 cm³, so that's 1000 litres.
![\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=1000000~cm^3\\ h=224~cm \end{cases}\implies \stackrel{cm^3}{1000000}=\pi r^2(\stackrel{cm}{224}) \\\\\\ \cfrac{1000000}{224\pi }=r^2\implies \sqrt{\cfrac{1000000}{224\pi }}=r\implies \cfrac{1000}{\sqrt{224\pi }}=r\implies \stackrel{cm}{37.7}\approx r](https://tex.z-dn.net/?f=%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%5C%5C%5C%5C%20V%3D%5Cpi%20r%5E2%20h~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20V%3D1000000~cm%5E3%5C%5C%20h%3D224~cm%20%5Cend%7Bcases%7D%5Cimplies%20%5Cstackrel%7Bcm%5E3%7D%7B1000000%7D%3D%5Cpi%20r%5E2%28%5Cstackrel%7Bcm%7D%7B224%7D%29%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B1000000%7D%7B224%5Cpi%20%7D%3Dr%5E2%5Cimplies%20%5Csqrt%7B%5Ccfrac%7B1000000%7D%7B224%5Cpi%20%7D%7D%3Dr%5Cimplies%20%5Ccfrac%7B1000%7D%7B%5Csqrt%7B224%5Cpi%20%7D%7D%3Dr%5Cimplies%20%5Cstackrel%7Bcm%7D%7B37.7%7D%5Capprox%20r)
now, we could have included the "cm³ and cm" units for the volume as well as the height in the calculations, and their simplication will have been just the "cm" anyway.