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Previous Year Question (PYQs)

If $x,\ 2x + 2,\ 3x + 3$ are in G.P., then the 4th term is:




Solution

For G.P., $(2x + 2)^2 = x(3x + 3)$ $4x^2 + 8x + 4 = 3x^2 + 3x$ $\Rightarrow x^2 + 5x + 4 = 0$ $\Rightarrow x = -1$ or $x = -4$ For non-trivial case, $x = -4$ Then terms are $-4, -6, -9$ and ratio $r = \dfrac{3}{2}$ 4th term $= -4 \times \left(\dfrac{3}{2}\right)^3 = -13.5$

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