Question

determine whether the sequence is an arithmetic sequence. justify your argument.
-10, -5, 0, 5, ...
this sequence select choice between its terms. this select choice an arithmetic sequence.
select choice
has a common difference of 0.5
has a common difference of 5
does not have a common difference

Explanation:

Step1: Recall the definition of an arithmetic sequence

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference, denoted as \( d \). The formula to find the common difference between the \( n \)-th term \( a_n \) and the \( (n - 1) \)-th term \( a_{n-1} \) is \( d=a_n - a_{n - 1} \).

Step2: Calculate the common difference for the given sequence

For the sequence \(-10,-5,0,5,\dots\):

• Calculate the difference between the second term and the first term: \( a_2 - a_1=-5-(-10)=-5 + 10 = 5 \)
• Calculate the difference between the third term and the second term: \( a_3 - a_2=0-(-5)=0 + 5 = 5 \)
• Calculate the difference between the fourth term and the third term: \( a_4 - a_3=5 - 0 = 5 \)

Since the difference between consecutive terms is constant (equal to 5), the sequence has a common difference of 5. And by the definition of an arithmetic sequence, a sequence with a constant common difference is an arithmetic sequence.

Answer:

First dropdown: has a common difference of 5
Second dropdown: is