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I am Lyosha [343]
3 years ago
8

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 t

he sequence is
Mathematics
2 answers:
Sedbober [7]3 years ago
8 0

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}

SpyIntel [72]3 years ago
4 0
t_{n}=243*3^{(n-1)}×
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