Answer:
No, the given sequence is not arithmetic.
Step-by-step explanation:
Given sequence-
- 5, - 1, 1, 5
Here, a = - 5, a is the first term of the given sequence.
For common difference-
d = [tex]t_{2} - t_{1} = t_{3} - t_{2} = t_{4} - t_{3}[/tex]
Let [tex]t_{1} = - 5, t_{2} = - 1[/tex]
d = [tex]t_{2} - t_{1}[/tex]
= - 1 -( - 5)
= - 1 + 5
= 4...........................(i)
Let [tex]t_{2} = - 1, t_{3} = 1[/tex]
d = [tex]t_{3} - t_{2}[/tex]
= 1-( - 1)
= 1 + 1
= 2................................(ii)
Let [tex]t_{3} = 1, t_{4} = 5[/tex]
d = [tex]t_{4} - t_{3}[/tex]
= 5 - 1
= 4....................................(iii)
∵ In equation (ii) common difference d is not 4, therefore the given sequence is not arithmetic.
