Question

the sum of three numbers in gp is 26 and their product is 216. find their terms​

Answer 1

Answer:

Let three terms of GP be [math]\frac{a}{r}, a, a*r[/math]

Their product will be

[math]\frac{a}{b} * a * a * r = 216[/math]

[math]a^3 = 216 = 6*6*6[/math]

[math]a= (6^3)^{1/3}[/math]

[math]a = 6[/math]

Now sum of these numbers

[math]\frac{a}{r} + a + a*r = 26[/math]

[math]\frac{a+ a*r + a*r^2}{r} = 26[/math]

[math]a + a*r + a*r^2 = 26r[/math]

Now putting value of a

[math]6 + 6r + 6r^2 = 26r[/math]

[math]6r^2 + 6r - 26r + 6 = 0[/math]

[math]6r^2 - 20r + 6 = 0[/math]

[math]2 ( 3r^2 - 10r + 3) =0[/math]

[math]3r^2 - 10r + 3 =0[/math]

[math]3r^2 - 9r - r +3 =0[/math]

[math]3r ( r - 3) - 1 (r - 3) = 0[/math]

[math](3r - 1) (r - 3) = 0[/math]

[math]r = \frac{1}{3} [/math]or[math] r =3[/math]

So GP will be

[math]a/r = 18 or 2[/math]

[math]a = 6[/math]

[math]a * r = 2 or 18[/math]

Therefore G.P will be

[math]18, 6, 2 or 2, 6, 18[/math]

Answer 2

Answer:

the sum of three numbers in gp is 26 and their product is 216. find their tterm's you have any questions or concerns please visit the plug-in settings please log in