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Home » Find the value of x such that, (i)     are three consecutive terms of a G.P. (ii)     are three consecutive terms of a G.P.
Find the value of x such that, (i)

    \[-\mathbf{2}/\mathbf{7},\text{ }\mathbf{x},\text{ }-\mathbf{7}/\mathbf{2}\]

are three consecutive terms of a G.P. (ii)

    \[\mathbf{x}\text{ }+\text{ }\mathbf{9},\text{ }\mathbf{x}\text{ }\text{ }\mathbf{6}\text{ }\mathbf{and}\text{ }\mathbf{4}\]

are three consecutive terms of a G.P.
Arithmetic and Geometric Progression | Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal
Find the value of x such that, (i)

    \[-\mathbf{2}/\mathbf{7},\text{ }\mathbf{x},\text{ }-\mathbf{7}/\mathbf{2}\]

are three consecutive terms of a G.P. (ii)

    \[\mathbf{x}\text{ }+\text{ }\mathbf{9},\text{ }\mathbf{x}\text{ }\text{ }\mathbf{6}\text{ }\mathbf{and}\text{ }\mathbf{4}\]

are three consecutive terms of a G.P.

From the question,

    \[\begin{array}{*{35}{l}} {{x}^{2}}~=\text{ }-2/7\text{ }\times \text{ }-7/2 \\ {{x}^{2}}~=\text{ }1 \\ x\text{ }=\text{ }\pm \text{ }1 \\ \end{array}\]

Therefore,

    \[x\text{ }=\text{ }1\text{ }or\text{ }x\text{ }=\text{ }\text{ }1\]

(ii)

    \[\mathbf{x}\text{ }+\text{ }\mathbf{9},\text{ }\mathbf{x}\text{ }\text{ }\mathbf{6}\text{ }\mathbf{and}\text{ }\mathbf{4}\]

are three consecutive terms of a G.P.

Solution:-

From the question,

    \[\begin{array}{*{35}{l}} {{\left( x\text{ }\text{ }6 \right)}^{2}}~=\text{ }\left( x\text{ }+\text{ }9 \right)\text{ }\times \text{ }4 \\ {{x}^{2}}~\text{ }12x\text{ }+\text{ }36\text{ }=\text{ }4x\text{ }+\text{ }36 \\ {{x}^{2}}~\text{ }12x\text{ }\text{ }4x\text{ }+\text{ }36\text{ }\text{ }36\text{ }=\text{ }0 \\ {{x}^{2}}~\text{ }16x\text{ }=\text{ }0 \\ x\left( x\text{ }\text{ }16 \right)\text{ }=\text{ }0 \\ \end{array}\]

Either let us take

    \[x\text{ }\text{ }16\text{ }=\text{ }16\]

    \[\begin{array}{*{35}{l}}</strong> <strong> Or\text{ }x\text{ }=\text{ }0 \\</strong> <strong> So,\text{ }x\text{ }=\text{ }0,\text{ }16 \\</strong> <strong>\end{array}\]

i

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