Question

The value of x for which the numbers 2x+1, 5x+1, and 11x+1 are in G.P is ___ (x is a natural number).

Answer 1

If a,b,c are in G.P, then $b^2$ = ac

Hence for 2x+1, 5x+1, and 11x+1 to be a G.P

$(5x+1{)}^2$ = (2x + 1)(11x + 1)

$25x^2$ + 10x + 1 = $22x^2$ + 13x + 1

$3x^2$ - 3x = 0

3x(x - 1) = 0

x = 0 or x = 1.

Hence, 2x+1, 5x+1, and 11x+1 are in G.P when x = 1.