If the fifth and eighth terms of an arithmetic sequence are minus 9 and minus 21, respectively, what are the first four terms of the sequence?

Question

Mathematics

Sidney Finley

15 February, 03:00

If the fifth and eighth terms of an arithmetic sequence are minus 9 and minus 21, respectively, what are the first four terms of the sequence?

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Answers (1)

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Larry Buckley · Answer 1

One way to do this problem is to determine the common difference. If the 5th and 8th terms are - 9 and - 21, we can do this by subtracting - 9 from - 21:

-21 - (-9) = - 12. The 5th and 8th terms are not consecutive, so we have to think in terms of (8-5), or 3, times the common difference to get from - 9 to - 21.

Note that - 12 divided by 3 is - 4. Thus, the common difference is - 4.

Check: - 9 - 4 = - 13; - 13 - 4 = - 17; - 17 - 4 = - 21 (which is correct).

We know that the 5th term is - 9. To find the 4th term, work backwards: subtract (-4) from - 9, which produces - 9+4=-5.

The fourth term is - 5. Subtracting - 4 from this (which is the same as adding 4 to this - 5) produces the third term; it is - 1. Can you now find the 2nd and 1st terms using the same approach?