The explicit function that defines the sequence is 15/2 - 9n/2
How to determine the explicit rule?
The sequence is given as:
3, -3/2, -6, -21/2
The above sequence is an arithmetic sequence, with the following parameters
- First term, a = 3
- Common difference, d = -9/2 i.e. -3/2 - 3
The explicit formula is then calculated as:
T(n) = a + (n -1) * d
This gives
T(n) = 3 +(n -1) * -9/2
Expand
T(n) = 3 + 9/2 - 9n/2
Evaluate
T(n) = 15/2 - 9n/2
Hence, the explicit function that defines the sequence is 15/2 - 9n/2
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