Question

Is -5, -1, 1, 5 arithmetic

Answer 1

No, the given sequence is not arithmetic.

Explanation:

Given sequence-

- 5, - 1, 1, 5

Here, a = - 5, a is the first term of the given sequence.

For common difference-

d =
`t_(2) - t_(1) = t_(3) - t_(2) = t_(4) - t_(3)`

Let
`t_(1) = - 5, t_(2) = - 1`

d =
`t_(2) - t_(1)`

= - 1 -( - 5)

= - 1 + 5

= 4...........................(i)

Let
`t_(2) = - 1, t_(3) = 1`

d =
`t_(3) - t_(2)`

= 1-( - 1)

= 1 + 1

= 2................................(ii)

Let
`t_(3) = 1, t_(4) = 5`

d =
`t_(4) - t_(3)`

= 5 - 1

= 4....................................(iii)

∵ In equation (ii) common difference d is not 4, therefore the given sequence is not arithmetic.