Check whether the following sequences are G.P. If so write tn. √5, 1

1.	Check whether the following sequences are G.P. If so write tn. √5, 1/√5, 1/5√5, 1/25√5,.........
Answer» \(\sqrt5,\frac1{\sqrt5},\frac1{5\sqrt5},\frac1{25\sqrt5},.....\) t₁ = √5, t₂ = 1/√5, t₃ = 1/5√5, t₄ = 1/25√5,..... Here, \(\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}=\frac15\) \(\because\) the ratio of any two consecutive terms is a constant, the given sequence is a Geometric progression. Here, a = √5, r = 1/5 t_n = ar^n-1 \(\therefore\) t_n = √5\((\frac15)^{n-1}\)

Check whether the following sequences are G.P. If so write tn. √5, 1/√5, 1/5√5, 1/25√5,.........

Answer»

\(\sqrt5,\frac1{\sqrt5},\frac1{5\sqrt5},\frac1{25\sqrt5},.....\)

t₁ = √5, t₂ = 1/√5, t₃ = 1/5√5, t₄ = 1/25√5,.....

Here, \(\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}=\frac15\)

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

Here, a = √5, r = 1/5

t_n = ar^n-1

\(\therefore\) t_n = √5\((\frac15)^{n-1}\)