An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To determine if the given sequence 7, 11, 15, 19 is arithmetic, we need to check the differences between its consecutive terms.
Let’s break it down:
- First term: 7
- Second term: 11
- Third term: 15
- Fourth term: 19
Now, we will calculate the differences:
- Difference between the second term (11) and the first term (7): 11 – 7 = 4
- Difference between the third term (15) and the second term (11): 15 – 11 = 4
- Difference between the fourth term (19) and the third term (15): 19 – 15 = 4
Since all the differences are the same, 4, we can conclude that the sequence is indeed arithmetic. Thus, the common difference of this arithmetic sequence is 4.
In summary, the sequence 7, 11, 15, 19 is an arithmetic sequence with a common difference of 4.