Question

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?

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?