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If the numbers \[\mathbf{n}\text{ }\text{ }\mathbf{2},\text{ }\mathbf{4n}\text{ }\text{ }\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{5n}\text{ }+\text{ }\mathbf{2}\] are in A.P., find the value of n.
If the numbers \[\mathbf{n}\text{ }\text{ }\mathbf{2},\text{ }\mathbf{4n}\text{ }\text{ }\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{5n}\text{ }+\text{ }\mathbf{2}\] are in A.P., find the value of n.
Arithmetic and Geometric Progression | Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal
If the numbers \[\mathbf{n}\text{ }\text{ }\mathbf{2},\text{ }\mathbf{4n}\text{ }\text{ }\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{5n}\text{ }+\text{ }\mathbf{2}\] are in A.P., find the value of n.

From the question it is given that, \[\mathbf{n}\text{ }\text{ }\mathbf{2},\text{ }\mathbf{4n}\text{ }\text{ }\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{5n}\text{ }+\text{ }\mathbf{2}\] are in A.P.

Multiplying by \[2\text{ }to\text{ }4n\text{ }\text{ }1\] then it becomes = \[8n\text{ }\text{ }2\]

So,

\[\begin{array}{*{35}{l}}

   8n\text{ }\text{ }2\text{ }=\text{ }n\text{ }\text{ }2\text{ }+\text{ }5n\text{ }+\text{ }2  \\

   8n\text{ }\text{ }2\text{ }=\text{ }6n  \\

   8n\text{ }\text{ }6n\text{ }=\text{ }2  \\

   2n\text{ }=\text{ }2  \\

   n\text{ }=\text{ }2/2  \\

   n\text{ }=\text{ }1  \\

\end{array}\]

i

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