Which sequence is an arithmetic sequence? option 1 of 4 3 , 4 , 7 , 11 , . . . 3 , 4 , 7 , 11 , . . . 3 , 4 , 7 , 11 , . . . 3 , 4 , 7 , 11 , . . . option 1 of 4 option 2 of 4 − 2 , 4 , − 8 , 16 , . . . − 2 , 4 , − 8 , 16 , . . . − 2 , 4 , − 8 , 16 , . . . − 2 , 4 , − 8 , 16 , . . . option 2 of 4 option 3 of 4 1 , 4 , 9 , 16 , . . . 1 , 4 , 9 , 16 , . . . 1 , 4 , 9 , 16 , . . . 1 , 4 , 9 , 16 , . . . option 3 of 4 option 4 of 4 − 3 , 0 , 3 , 6 , . . . − 3 , 0 , 3 , 6 , . . . − 3 , 0 , 3 , 6 , . . . − 3 , 0 , 3 , 6 , . . . option 4 of 4
Question
Which sequence is an arithmetic sequence? option 1 of 4 3 ,
4 ,
7 ,
11 ,
.
.
. 3 ,
4 ,
7 ,
11 ,
.
.
.
3 ,
4 ,
7 ,
11 ,
.
.
. 3 ,
4 ,
7 ,
11 ,
.
.
. option 1 of 4 option 2 of 4 − 2 ,
4 , − 8 ,
16 ,
.
.
. − 2 ,
4 , − 8 ,
16 ,
.
.
.
− 2 ,
4 , − 8 ,
16 ,
.
.
. − 2 ,
4 , − 8 ,
16 ,
.
.
. option 2 of 4 option 3 of 4 1 ,
4 ,
9 ,
16 ,
.
.
. 1 ,
4 ,
9 ,
16 ,
.
.
.
1 ,
4 ,
9 ,
16 ,
.
.
. 1 ,
4 ,
9 ,
16 ,
.
.
. option 3 of 4 option 4 of 4 − 3 ,
0 ,
3 ,
6 ,
.
.
. − 3 ,
0 ,
3 ,
6 ,
.
.
.
− 3 ,
0 ,
3 ,
6 ,
.
.
. − 3 ,
0 ,
3 ,
6 ,
.
.
. option 4 of 4
Solution
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.
Let's check each option:
Option 1: 3, 4, 7, 11... The differences between consecutive terms are 1, 3, 4, which are not constant. So, this is not an arithmetic sequence.
Option 2: -2, 4, -8, 16... The differences between consecutive terms are 6, -12, 24, which are not constant. So, this is not an arithmetic sequence.
Option 3: 1, 4, 9, 16... The differences between consecutive terms are 3, 5, 7, which are not constant. So, this is not an arithmetic sequence.
Option 4: -3, 0, 3, 6... The differences between consecutive terms are 3, 3, 3, which are constant. So, this is an arithmetic sequence.
Therefore, the sequence in option 4 is an arithmetic sequence.
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