## Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference. -8, -11, -14, -17, …

Question

Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference.

-8, -11, -14, -17, …

A.Yes the common difference is -3

B.Yes the common difference is 3

C.No there is no common difference

D.Yes the common difference is 8/11

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6 days 2021-10-12T10:51:42+00:00 1 Answer 0

A. Yes, the common difference is -3

Step-by-step explanation:

First of all, this would be an arithmetic sequence, because there is a constant value being added (or effectively subtracted, if the value is negative) to each subsequent number in the sequence.

To find the common difference, ie. what value is added, we must take a term from the sequence and subtract the previous term from it.

Using the first two terms, -8 and -11:

-11 – (-8) = -11 + 8

= -3

You can check if this is right by taking another term from the sequence and trying to add the common difference, then seeing if this value matches the next term.

Taking the third and fourth terms, -14 and -17:

– 14 + (-3) = -14 – 3

= -17

The fourth term is also -17.

This is correct; thus, it is an arithmetic sequence, with a common difference of -3 (answer A)

It is a common mistake for people to answer B, however always remember that what we are looking for is what value, added to a given term, will give us the next term.

Since adding a negative number effectively means subtracting it, then this will apply to sequences that become more negative (or decrease) rather than more positive (or increase).

Also remember to use brackets in order to clearly set out working as this can lead to little mistakes, particularly where many negative signs are involved.

Hope that helped 🙂