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in an arithmetic sequence, term 10 is 33 and term 22 is -3. What are the first 4 terms

Sagot :

sqdancefan

9514 1404 393

Answer:

  60, 57, 54, 51, ...

Step-by-step explanation:

The general term of an arithmetic sequence is ...

  an = a1 +d(n -1)

We would like to find the first term (a1) and the common difference (d). We can use the two given terms to find these parameters.

  a10 = 33 = a1 +d(10 -1)

  a22 = -3 = a1 +d(22 -1)

Subtracting the first equation from the second, we get ...

  (-3) -(33) = (a1 +21d) -(a1 +9d)

  -36 = 12d

  -3 = d

Using this value in the first equation, we can find a1.

  33 = a1 +9(-3) = a1 -27

  60 = a1 . . . . . . . . . . . . . . add 27 to both sides

So, our sequence has first term 60 and a common difference of -3.

The first 4 terms are ...

  60, 57, 54, 51, ...

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