Question

Is the sequence arithmetic? If yes, determine the common difference. *

(1 Point)
-14-9, -4, 1, 6, ...
O no, it does not increase or decrease the exact same amount
O yes, d = 5
O yes, d = -5

Answer 1

Option 2: Yes, d= 5 is the correct answer

Explanation:

An arithmetic sequence is a sequence where the common difference between the consecutive terms is same.

Given arithmetic sequence is:

-14, -9, -4, 1, 6

To check if it is an arithmetic sequence, we have to find the common difference d

`a_1 = -14\\a_2 = -9\\a_3 = -4\\a_4 = 1`

Now,

`d = a_2-a_1 = -9-(-14) = -9+14 = 5\\d = a_3 - a_2=-4-(-9) = -4+9 = 5\\d = a_4-a_3 = 1-(-4) = 1+4 = 5`

As the common difference is same, the given sequence is an arithmetic sequence.

Hence,

Option 2: Yes, d= 5 is the correct answer