Answer
The sequence is not arithmetic
Work Step by Step
A sequence is arithmetic when there is a pattern observed in the sequence.
A sequence is not arithmetic when there is no pattern observed in the sequence.
A pattern is observed in the sequence when the change between consecutive terms are the same.
We are given the sequence as:
1, -7, -14, -21, ...
Let's find the difference between consecutive terms:
2nd term and 1st term: $-7 -1= -8$
3rd term and 2nd term: $ -14-(-7)= -14+7=-7$
4th term and 3rd term: $ -21-(-14)= -21+14=-7$
The difference between the 2nd and 1st term is not the same as the difference between the 3rd and 4th term or the 2nd and 3rd term, so there is no pattern observed in this sequence.
This means that the sequence is not arithmetic
