Question

Is this an arithmetic sequence ? Why ?

Hint:

Any sequence generated by the rule "numbers that leave a remainder 'r' when divided by 'd'" will always be an arithmetic progression with a common difference of 'd'.

Answer 1

We need to determine if the sequence 1, 5, 9, 13, ... is an arithmetic sequence and provide a reason.

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. This constant difference is called the common difference (d).

Let's check the difference between consecutive terms in the sequence:
- Difference between the 2nd and 1st term: 5 - 1 = 4.
- Difference between the 3rd and 2nd term: 9 - 5 = 4.
- Difference between the 4th and 3rd term: 13 - 9 = 4.
Since the difference is always 4, there is a constant common difference.

Yes, this is an arithmetic sequence. The reason is that there is a common difference of 4 between any two consecutive terms.