Question

Q3.

3, x, x+6.... Are three consecutive terms in a geometric sequence I) find possible values for x if x is positive.​

Answer 1

x = 6

Explanation:

The ratio of consecutive terms is the same, so we have ...

x/3 = (x +6)/x

x^2 = 3(x +6) . . . . . . multiply by 3x

x^2 -3x -18 = 0 . . . . subtract 3(x+6), simplify

(x -6)(x +3) = 0 . . . . factor

x = 6 . . . . . . . . . the only possible positive value

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Additional comment

The zero product rule tells you that a product will be zero if and only if a factor is zero. That is, the solutions to this equation are values of x that make the factors zero: x = 6, x = -3.