The ninth and tenth term of the given arithmetic sequence are: -18 and -21.
A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Now,
Given: 6, 3, 0, -3, ....; it is a decreasing AP.
Here, a = 6 (initial term) and d = -3 (common difference)
Thus, in the formula: [tex]a_n[/tex] = a + (n - 1) d, substituting these values:
=> [tex]a_n[/tex] = 6 + (n - 1)(-3)
For ninth term, n = 9
Thus, [tex]a_n[/tex] = [tex]a_9[/tex] = 6 + (9 - 1)(-3)
=> [tex]a_9[/tex] = 6 + (8)(-3)
=> [tex]a_9[/tex] = 6 -24
=> [tex]a_9[/tex] = -18
Similarly, for the tenth term, n = 10
Thus, [tex]a_n=a_{10}[/tex] = 6 + (10 -1) (-3)
=> [tex]a_{10}[/tex] = 6 + (9) (-3)
=> [tex]a_{10}[/tex] = 6 - 27
=> [tex]a_{10}[/tex] = -21
Hence, The ninth and tenth term of the given arithmetic sequence are: -18 and -21.
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