Question

Which sequence represents an arithmetic sequence?

−5, −7, −10, −14, −19, …
1.5, −1.5, 1.5, −1.5, …
4.1, 5.1, 6.2, 7.2, …
−1.5, −1, −0.5, 0, …

Answer 1

we know that

arithematic sequence will always have common difference

(a)

−5, −7, −10, −14, −19, …

we can see that

`d_1=-7+5=-2`

`d_2=-10+7=-3`

they are not equal

so, this is not arithematic sequence

(2)

1.5, −1.5, 1.5, −1.5, …

we can see that

`d_1=-1.5-1.5=-3`

`d_2=1.5+1.5=3`

they are not equal

so, this is not arithematic sequence

(3)

4.1, 5.1, 6.2, 7.2, …

we can see that

`d_1=5.1-4.1=1`

`d_2=6.2+5.1=1.1`

they are not equal

so, this is not arithematic sequence

(4)

−1.5, −1, −0.5, 0, …

we can see that

`d_1=-1+1.5=0.5`

`d_2=-0.5+1=0.5`

they are equal

so, this is arithematic sequence