4n term of the geometric progression x, x2+2, x3+10 is

Question

4n term of the geometric progression x, x2+2, x3+10 is (A) 0 (B) 6 (C) 54 (D) 27

Tardigrade Admin · Accepted Answer

Given G.P. is x , x 2+2, x 3+10 ∴ (x2+2)2=x(x3+10) ⇒ 4 x2-10 x+4=0 ⇒ 2 x2-5 x+2=0 ⇒(2 x-1)(x-2)=0 ∴ x=2,1 / 2 For x=2 G.P. is 2, 6, 18, 54 so next term of G.P. is 54

Q. $4^{n}$ term of the geometric progression $x, x^{2} + 2, x^{3} + 10$ is

0

6

54

27

Given G.P. is $x, x^{2} + 2, x^{3} + 10$
$∴ (x^{2} + 2)^{2} = x (x^{3} + 10)$
$\Rightarrow 4 x^{2} - 10 x + 4 = 0$
$\Rightarrow 2 x^{2} - 5 x + 2 = 0$
$\Rightarrow (2 x - 1) (x - 2) = 0$
$∴ x = 2, 1/2$
For $x = 2$
G.P. is $2, 6, 18, 54$
so next term of G.P. is $54$

Q. 4n term of the geometric progression x,x2+2,x3+10 is

0

6

54

27

Given G.P. is x,x2+2,x3+10 ∴(x2+2)2=x(x3+10) ⇒4x2−10x+4=0 ⇒2x2−5x+2=0 ⇒(2x−1)(x−2)=0 ∴x=2,1/2 For x=2 G.P. is 2,6,18,54 so next term of G.P. is 54

Q. $4^{n}$ term of the geometric progression $x, x^{2} + 2, x^{3} + 10$ is

Given G.P. is $x, x^{2} + 2, x^{3} + 10$
$∴ (x^{2} + 2)^{2} = x (x^{3} + 10)$
$\Rightarrow 4 x^{2} - 10 x + 4 = 0$
$\Rightarrow 2 x^{2} - 5 x + 2 = 0$
$\Rightarrow (2 x - 1) (x - 2) = 0$
$∴ x = 2, 1/2$
For $x = 2$
G.P. is $2, 6, 18, 54$
so next term of G.P. is $54$