Given that (x + 2), (4x + 3) and (7x + 24) are consecutive terms of a Geometric Progression (G.P), find the; (a) value of x; (b) common ratio.

Here are the solutions for questions 6 and 7.

Question 6:
Given that $(x+2)$, $(4x+3)$ and $(7x+24)$ are consecutive terms of a Geometric Progression (G.P.).

For a Geometric Progression, the square of the middle term is equal to the product of the first and third terms. Let the terms be $a_1 = x+2$, $a_2 = 4x+3$, and $a_3 = 7x+24$.
So, $a_2^2 = a_1 a_3$.

Step 1: Set up the equation using the G.P. property.

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