Question

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

Answer 1

$\textbf{ Geometric progression}$ : A series in which ratio of consecutive terms is constant.

If a, b, c are three consecutive terms of a geometric progression, then b² = a * c.

So, If x, x + 2 , x + b are consecutive terms of G. P then,

( x + 2 )² = x ( x + b )

x² + 4 + 4x = x² + bx

4 + 4x = bx

x ( 4 - b) = -4

x = 4/ ( b - 4 )

Therefore, The value of x = $\frac{4}{(b-4)}$

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