Question

In a GP the 3^rd term is 24 and the 6^th term is 192. Find the 10^th term.

Answer 1

\[\text { Let a be the first term and r be the common ratio } . \]

\[ \therefore a_3 = 24 \text { and } a_6 = 192\]

\[ \Rightarrow a r^2 = 24 \text { and } a r^5 = 192\]

\[ \Rightarrow \frac{a r^5}{a r^2} = \frac{192}{24}\]

\[ \Rightarrow r^3 = 8 \]

\[ \Rightarrow r^3 = 2^3 \]

\[ \Rightarrow r = 2\]

\[\text { Putting } r = 2 \text { in a }r^2 = 24\]

\[a \left( 2 \right)^2 = 24 \]

\[ \Rightarrow a = 6\]

\[\text { Now}, {10}^{th}\text { term  }= a_{10} = a r^9 \]

\[\text { Putting a = 6 and r = 2 in } a_{10} = a r^9 \]

\[ \Rightarrow a_{10} = \left( 6 \right) \left( 2 \right)^9 = 3072\]

\[\text { Thus, the } {10}^{th}\text { term of the G.P. is } 3072 .\]