Is the sequence an=8n-14 arithmetic?
Your answer is (input yes or no)__??__ ;
if your answer is yes,
its first term is__??__ .
its common difference is__??__ .
To determine whether the sequence an=8n-14 is arithmetic, we need to check if the difference between consecutive terms is constant.
The formula for an arithmetic sequence is an = a1 + (n-1)d, where a1 represents the first term and d represents the common difference.
To find the first term, we substitute n = 1 into the given formula:
a1 = 8(1) - 14
a1 = -6
To find the difference between consecutive terms, we substitute n = 2 and n = 1 into the given formula:
a2 = 8(2) - 14
a2 = 2
Now, we can calculate the common difference by subtracting the first term from the second term:
d = a2 - a1
d = 2 - (-6)
d = 8
Since the common difference between consecutive terms is 8 (which is a constant value), we can conclude that the sequence an=8n-14 is indeed arithmetic.
Therefore, the answers to the questions are:
- Is the sequence arithmetic? Yes.
- First term: -6.
- Common difference: 8.