Question

Which of the sequences is an arithmetic sequence?

Answer 1

The sequence -2, -8, -14, -20, -26 is an A.P

Option A is correct

Explanation:

Given the sequence we have to choose the option which is an arithmetic sequence.

In A.P, the common difference i.e d remains the same

`d=x_2-x_1=x_3-x_2`

Option A: -2, -8, -14, -20, -26, ...

`x_2-x_1=-14-(-8)=-14+8=-6`

`x_3-x_2=-20-(-14)=-20+14=-6`

which is same hence A.P

Option B: -48, -24, -12, -6, -3,...

`x_2-x_1=-24-(-48)=-24+48=24`

`x_3-x_2=-12-(-24)=-12+24=-12`

which is not same hence not an A.P

Option C: -2, 6, -10, 14, -18,...

`x_2-x_1=6-(-2)=6+2=8`

`x_3-x_2=-10-6=-16`

which is NOT same hence not an A.P

Option D: 1, 6, 12, 18, 24,..

`x_2-x_1=6-1=5`

`x_3-x_2=12-6=6`

which is not same hence not an A.P

Answer 2

Sequence A is the only one with a common difference (-6).

_____

Sequence D comes close, but its first difference is 5 while the others are 6. Hence there is no common difference.