Identify the missing terms in the given arithmetic sequence.
5, ?, ?, ?, -9.

the whole sequence is

5, 1 1/2, -2, -5 1/2, -9

the missing elements were

1 1/2, -2, -5 1/2

Step-by-step explanation:

an arithmetic sequence means that there is always constant added or subtracted from the previous term to create the next term.

we know, we need to go 4 steps or terms to get from 5 to -9.

5 + c = ?

5 + c + c = ??

5 + c + c + c = ???

5 + c + c + c + c = -9

5 + 4c = -9

4c = - 14

c = -14/4 = -7/2

so, we get

? = 5 + -7/2 = 10/2 - 7/2 = 3/2 = 1 1/2

?? = 3/2 - 7/2 = -4/2 = -2

??? = -4/2 - 7/2 = -11/2 = -5 1/2

and the next step is -11/2 - 7/2 = -18/2 = -9

correct.

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