blitzbabeiy

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?

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${a}_{n}=\{\begin{array}{l}3{a}_{n-2},if\text{}n\text{}is\text{}odd\\ {a}_{n-2}+10,if\text{}n\text{}is\text{}even\end{array}$ for all $n\ge 3$

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

thus, the relation of the given sequence is

and

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