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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, ...