Math

QuestionWhich arithmetic sequence has a common difference of 3? A) n+1,n+4,n+7,n+10n+1, n+4, n+7, n+10 B) 0,3n,6n,9n0,3n,6n,9n C) n,3n,9n,27nn,3n,9n,27n D) n+3,n+9,n+27,n+81n+3,n+9,n+27,n+81

Studdy Solution

STEP 1

Assumptions1. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference. . We are looking for an arithmetic sequence with a common difference of3.

STEP 2

Let's examine each option individually to determine which one forms an arithmetic sequence with a common difference of.
Option A n+1,n+4,n+7,n+10,n+1, n+4, n+7, n+10, \ldots

STEP 3

Calculate the difference between the second term and the first term in Option A.
Difference=(n+)(n+1)Difference = (n+) - (n+1)

STEP 4

implify the difference.
Difference=n+4n1=3Difference = n+4 - n -1 =3

STEP 5

The difference between the second term and the first term in Option A is3, which is the common difference we are looking for. Therefore, Option A is the correct answer.
The arithmetic sequence with a common difference of3 is n+1,n+4,n+7,n+10,n+1, n+4, n+7, n+10, \ldots.

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