Question

Which of the following is an arithmetic sequence?

Answer 1

Explanation:

The given above is an arithmetic sequence with first term equal to 3 and the common difference equal to 4. That is from 7 - 3 = 11 - 7 = 15 - 11. The nth term of an arithmetic sequence is given by the equation,

an = a1 + (n - 1) x d

Substituting the given,

an = 3 + 4(n - 1)

thus, the answer is the fourth choice.

Answer 2

Option C is the correct answer.

Explanation:

Option A:

`\texttt{Term 2 - Term 1 = }(6)/(11)-\left ( -(7)/(11)\right )=(13)/(11)\\\\\texttt{Term 3 - Term 2 = }-(5)/(11)-(6)/(11)=-(11)/(11)`

Common difference is not same, not an arithmetic sequence.

Option B:

`\texttt{Term 2 - Term 1 = }-(3)/(5)-\left ( -(3)/(4)\right )=(3)/(4)-(3)/(5)=(3)/(20)\\\\\texttt{Term 3 - Term 2 = }-(3)/(6)-\left ( -(3)/(5)\right )=(3)/(5)-(3)/(6)=(3)/(30)=(1)/(10)`

Common difference is not same, not an arithmetic sequence.

Option C:

`\texttt{Term 2 - Term 1 = }2-(1)/(2)=(3)/(2)\\\\\texttt{Term 3 - Term 2 = }(7)/(2)-2=(3)/(2)\\\\\texttt{Term 4 - Term 3 = }5-(7)/(2)=(3)/(2)`

Common difference is same, an arithmetic sequence.

Option D:

`\texttt{Term 2 - Term 1 = }-(3)/(2)-(3)/(4)=-(18)/(8)=-(9)/(4)\\\\\texttt{Term 3 - Term 2 = }3-\left ( -(3)/(2)\right )=(9)/(2)`

Common difference is not same, not an arithmetic sequence.

Option C is the correct answer.