19)In a G.P. 729, 243, 81,... find \(t_7\)

19)In a G.P. 729, 243, 81,... find \(t_7\)

Answer: \(n^{th}\) term of G.P = \(ar^{n-1}\)

Here a = 729

\(r = \frac{t_2}{t_1} = \frac{243}{729} = \frac{1}{3}\)

\(t_7 = ar^{7-1} = ar^6 = 729 \left(\frac{1}{3}\right)^6\)

\(= 729 \times \frac{1}{729} = 1\)

\(t_7 = 1\)