Question

Find x ßo that x, x+2, x+6 are consecutive terms og a geometric progression

Answer 1

Answer :

x = 2

Explanation:

Let a= x ,b = x+2 , c = x+6

Now ,

b² = ac

[ Since , a,b and c are in

G.P]

=> (x+2)² = x(x+6)

=> x²+4x+4 = x²+6x

=> 4 = x²+6x-x²-4x

=> 4 = 2x

=> (4/2) = x

=> 2 = x

Therefore,

x = 2

••••

Answer 2

Answer:

X = 2.

Step-by-step explanation:

G.P. a, a2, a3, a4, ....

r = a2/a1 = a3/a2 = a4/a3 = K

tn = ar^n - 1

a, ar, ar^2

$(ar) {}^{2} = a \times ar {}^{2}$

G.P. if a, b, c are G.P. then

$\: \: \: \: \: \: \: b {}^{2} = ac$

$(x + 2) {}^{2} = x(x + 6)$

$x {}^{2} + 4x + 4 = x {}^{2} + 6x$

$2x = 4$

$x = 2$

∴ X = 2.

@Genius