Check whether the following sequences are G.P. If so, write tn. 2, 6,

1.	Check whether the following sequences are G.P. If so, write tn. 2, 6, 18, 54, ……
Answer» 2, 6,18, 54,.... t₁ = 2, t₂ = 6, t₃ = 18, t₄ = 54,... Here, \(\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}\) = 3 \(\because\) the ration of any two consecutive terms is a constant, the given sequence is a Geometric progression. Here, a = 2, r = 3 t_n = ar^n-1 ^{\(\therefore\)}t_n = 2(3^n-1)

Check whether the following sequences are G.P. If so, write tn. 2, 6, 18, 54, ……

Answer»

2, 6,18, 54,....

t₁ = 2, t₂ = 6, t₃ = 18, t₄ = 54,...

Here, \(\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}\) = 3

\(\because\) the ration of any two consecutive terms is a constant, the given sequence is a Geometric progression.

Here, a = 2, r = 3

t_n = ar^n-1

^{\(\therefore\)}t_n = 2(3^n-1)