Given an arithmetic sequence -2,-13,-24, . . . , the recursive formula is: a(n) = a(n-1) -11 and the explicit formula is a(n) = 9 - 11n
Suppose we are given an arithmetic sequence:
a(1), a(2), a(3), a(4), ....
Then, in an arithmetic sequence, the next term is obtained by adding a constant to the previous term. This constant is called a common difference.
Let d = common difference, then
a(2) = a(1) + d
a(3) = a(2) + d
and so on, until
a(n) = a(n-1) + d
This is a recursive formula. Here a(n) = nth term, and a(n-1) = (n-1)th term.
The sequence in the problem:
-2,-13,-24, . .
Notice that:
-13 = -2 + (-11)
-24 = -13 + ( -11)
Hence, d = -11, and therefore, the recursive formula for the nth term is:
a(n) = a(n-1) -11
To find the nth term, we can also use the explicit formula:
a(n) = a(1) + (n-1).d
In the given sequence, a(1) = -2, and d = -11. Substitute these parameters:
a(n) = -2 + (n-1) . (-11)
= -2 - 11n + 11
= 9 - 11n
Thus, the explicit formula is a(n) = 9 - 11n.
Learn more about arithmetic sequences here:
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