Question

A geometric sequence is defined by a the recursive formula t1 = 243, tn + 1 = tn 3 , where n ∈N and n ≥ 1. The general term of the sequence is

Answer 1

$t_{n}=243*3^{(n-1)}$×

Answer 2

Answer:

$T_n = 243 \times 3^{n-1}$

Step-by-step explanation:

Given : $t_1=243$

Expression :$t_{n+1}=3t_n$

Put n = 1

$t_{1+1}=3\times t_1$

$t_{2}=3\times 243$

$t_{2}=729$

Put n = 2

$t_{2+1}=3\times t_2$

$t_{3}=3\times729$

$t_{3}=2187$

Put n = 3

$t_{3+1}=3\times t_3$

$t_{4}=3\times2187$

$t_{4}=6561$

Continuing in this manner we will get the geometric sequence :

243,729,2187,6561 ........

Formula for nth term of G.P. :$T_n = ar^{n-1}$

a= 243

r = common ratio between the consecutive terms .

$r=\frac{729}{243}=\frac{2187}{729}=3$

Substituting values in the formula :

$T_n = 243 \times 3^{n-1}$

Hence the general term of the sequence is $T_n = 243 \times 3^{n-1}$