Best solutions to - "The infinite sequence will be defined as recurrent..."

blitzbabeiy

Answered question

2022-01-22

The infinite sequence will be defined as recurrent relation:

1, 10, 3, 20, 9, 30, 27, 40, \dots

The sequence is a composition of some arithmetic and/or geometric sequences. How many elements will become non-recurrent part?

Jordyn Horne

Beginner2022-01-23Added 16 answers

We have the sequence

1, 10, 3, 20, 9, 30, 27, 40, \dots

a_{1} = 1

a_{2} = 10

a_{3} = 3 = 3 a_{1} = 3 a_{3 - 2}

a_{4} = 20 = a_{2} + 10 = a_{4 - 2} + 10

a_{5} = 9 = 3 a_{3} = 3 a_{5 - 2}

a_{6} = 30 = a_{4} + 10 = a_{6 - 2} + 10

a_{7} = 27 = 3 a_{5} = 3 a_{7 - 2}

a_{8} = 40 = a_{6} + 10 = a_{8} - 2 + 10

thus, the relation of the given sequence is

a_{1} = 1

a_{2} = 10

and

a_{n} = {\begin{cases} 3 a_{n - 2}, i f n i s o d d \\ a_{n - 2} + 10, i f n i s e v e n \end{cases}

for all

n \geq 3

Hence, we can say that 2 elements will become non-recurrence part. Answer is 2

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