Question

I'm stumped on how to do this, it's worth 10 points and I'll give you Brainliest if you answer right
Maria creates a sequence of integers where the first and second terms are both 1. At each step she adds the last two terms she has obtained. If the sum is less than 9, then she enters that sum as her new term. Otherwise she subtracts 8 from the sum and records that. Her sequence therefore starts 1, 1, 2, 3, 5, 8, 5, 5, . . . Find the 2020th term in the sequence.

Answer 1

Answer:

The 2020th term is 3

Step-by-step explanation:

Recursive Sequence

We are given a recursive and conditional sequence where each term depends on two previous terms and a rule.

Each term is the sum of the two previous terms. But if that sum exceeds 8, then 8 is subtracted.

The first terms are, therefore:

1, 1, 2, 3, 5, 8, 5, 5, 2, 7, 1, 8, 1, 1, 2, 3, 5, 8, 5, 5, 2, 7, 1, 8, ....

Note the sequence repeats itself at term 13, that is:

a13=a1, a14=a2, a15=a3 and so on.

To find any given term, it's just a matter of calculating the remainder of that number of the term divided by 12.

For example, the term number 100 is calculated by dividing 100/12=8 (only the integer part).

Since 8*12=96, the remainder is 100-96=4

Thus, a100=a4=3

The term 2020 is calculated now:

2020/12 = 168 (integer only)

168*12=2016

The remainder is 2020-2016=4, thus

a2020 = a4 = 3

The 2020th term is 3