Question

Is the following sequence arithmetic? If so, identify the common difference. –16, –22, –29, –37, . . .

Answer 1

No, this is not an arithmetic sequence.

(-22)-(-16)= -6
(-29)-(-22)= -7
(-37)-(-29)= -8

Answer 2

Answer: No, the given sequence is not arithmetic.

Step-by-step explanation: We are given to check whether the following sequence is ARITHMETIC or not :

–16, –22, –29, –37, . . .

If so, we are to find the common difference.

ARITHMETIC SEQUENCE : A sequence is said to be arithmetic if the difference between any two consecutive terms is same.

For the given sequence, we have

`\textup{2nd term}-\textup{1st term}=-22-(-16)=-22+16=-6,\\\\\textup{3rd term}-\textup{2nd term}=-29-(-22)=-29+22=-7,\\\\\textup{4th term}-\textup{3rd term}=-37-(-29)=-37+29=-8,etc.`

Therefore, the difference between any two consecutive terms are not same.

Thus, the given sequence is not ARITHMETIC.