Question

Find x so that x,x+2,x+6 are consecutive terms of a geometric progression

Answer 1

When a,b,c are in gp, ac=b²

so, (x+2)²=x(x+6)

Answer 2

The value of x that has to be found is 2.

Step-by-step explanation:

Given:

Find x so that x, x+2, x+6 are consecutive terms of a geometric progression

Solution:

In a GP, ac = $b^2$

Here,

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

ac = $b^2$

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

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

6x = 4 + 4x

2x = 4

X = 2

To know more;

For each geometric progression find the common ratio ‘r’, and then find an(i) 3, 3/2, 3/4, 3/8, ......... (ii) 2, −6, 18, −54(iii) −1, −3, −9, −18 .... (iv) 5, 2, 4/5, 8/25, .........

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