Question

Which arithmetic sequence has a common difference of 3? A) 0, 3n, 6n, 9n, ... B) n, 3n, 9n, 27n, ... C) n + 1, n + 4, n + 7, n + 10, ... D) n + 3, n + 9, n + 27, n + 81,

Answer 1

Option C is correct.

Explanation:

Given the arithmetic sequence. we have to choose that arithmetic sequence which has the common difference of 3.

Option A: 0, 3n, 6n, 9n, ...

The above sequence gives the common difference

3n-0=6n-3n=9n-6n=3n

Option B: n, 3n, 9n, 27n, ...

The above sequence does not give the same difference. Hence, not AP

Option C: n + 1, n + 4, n + 7, n + 10, ...

The above sequence gives the common difference

n+1-0=n+4-(n+1)=3

Option D: n + 3, n + 9, n + 27, n + 81

The above also sequence does not give the same difference. Hence, not AP.

Hence, option C is correct.