Question

Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. –5, –11, –17, –23, –29, . . .

Answer 1

an aritmetic sequence increases by the same amount each time (if it decreases, then it increases by a negative number)

the common difference is the number that must be added to a term to get the next term

let's see if it increases by the same amount

-5 to -11 is increase of -6

-11 to -17 is increase of -6

-17 to -23 is increase of -6

-23 to -29 is increase of -6

so it appears to be aritmetic

common difference is -6

-29-6=-35

-35-6=-41

-41-6=-47

the next 3 terms are -35, -41, -47