5. A sequence starts with number 2021. The following cyclic operations are performed again and again in this order to generate the next terms of the sequence: • Multiply by 2, Add 2, Divide by 2, Subtract 2 ; • Again: Multiply by 2, Add 2, Divide by 2, Subtract 2 ; • Again: Multiply by 2, Add 2, Divide by 2, Subtract 2 ; and so on... The sequence will be: 2021, 4042, 4044, 2022, 2020, 4040, 4042, ... The sequence stops with 0 finally, once it (zero) is reached. The total number of terms in this sequence will be
Answers
The Total number of terms in this sequence will be 8085.
Step-by-step explanation:
Here,
1st term is - 2021; 2nd term is - 4042; 3rd term is 4044; 4th term is 2022;
5th term is -2020; 6th term is 4040; 7th term is 4042; 8th term is 2021;
9th term is - 2019.
The above sequence clearly shows that after every 4th term the number of the value is decreasing 1. This sequence follows the pattern of 4n+1.
Here the n= the value of first term- the number we want to know its term.
In this sequence the value of first term is=2021.
The number we want to know its term is=0.
Therefore n=2021-0
n=2021.
The pattern of the sequence= 4n+1
=(4*2021)+1
=8084+1
the total number of terms in the sequence will be = 8085.