The recursive sequence is defined by the formula t_n=2t_(n−1)+3; and t_1=−2, how do you find t_6?

priscillianaw1

priscillianaw1

Answered question

2022-10-02

The recursive sequence is defined by the formula t n = 2 t n - 1 + 3 ; and t 1 = - 2 , how do you find t 6 ?

Answer & Explanation

Frederick Espinoza

Frederick Espinoza

Beginner2022-10-03Added 7 answers

Proposing t n = c 0 a n + b and substituting we get
c 0 a n + b = 2 ( c 0 a n - 1 + b ) + 3 or
c 0 a n - 2 c 0 a n - 1 = 2 b - b + 3
Making a=2 and b=−3 the equality is observed. So we get
t n = c 0 2 n - 3 and also
t 1 = c 0 2 1 - 3 c 0 = 1 2 . Putting all together
t n = 2 n - 1 - 3 t 6 = 2 5 - 3

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